Associate Professor Jeffrey Hogan
Associate Professor
School of Mathematical and Physical Sciences (Mathematics)
 Email:jeff.hogan@newcastle.edu.au
 Phone:(02) 4921 7235
Career Summary
Biography
Biography
I was awarded the BSc (Hons) in 1985 and the PhD in 1990 (under the supervision of Professors John Price and Michael Cowling) from the University of New South Wales. After completing my study, I held postdoctoral positions at the University of Texas at Austin (198991) with Professor John Gilbert, Flinders University (199193) with Professor Garth Gaudry and Macquarie University (19932000) with Professor Alan McIntosh. I then moved to the University of Arkansas in Fayetteville, and gained tenure and promotion to Associate Professor in 2006. In 2009 I accepted a position at the University of Newcastle.
Research
Broadly speaking, I work in pure, applied and computational harmonic analysis. My past and present projects include:
 Uncertainty Principles for the Fourier transform on locally compact groups
 Singular integrals and wavelet frames
 Sampling theory in Fourier and wavelet analysis
 CliffordFourier theory
 Bandlimited and bandpass prolate functions in one and higher dimensions
 Applications of optimisation in the construction of one and multidimensional wavelets
Research Collaboration
I have active collaborations with:
 Professor Joseph Lakey (New Mexico State University)
 Dr Matthew Tam (University of Goettingen)
 Dr Peter Massopust (Technical University of Munich)
 Professor Brigitte Forster (University of Passau)
 Dr Daniel Abreu (Acoustics Research Institute, Vienna)
 Dr JoseLuis Romero (University of Vienna)
 Dr Mark Craddock (University of Technology Sydney)
Teaching
Since arrival at UON, I have taught across the undergraduate mathematics curriculum, including courses in firstyear calculus, multivariable calculus, linear algebra, mathematical modelling, differential equations, complex analysis, numerical analysis and my favourite  Fourier analysis.
Administration
Administrative duties at UON have included:
 Deputy Head of School of Mathematical and Physical Sciences: 2015  present
 Acting Head of Mathematics Discipline: July 2017  July 2018
 MAPS HDR Coordinator: January 2017  present
 Bachelor of Mathematics Convenor: 2009  2012
Qualifications
 PhD, University of New South Wales
 Bachelor of Science, University of New South Wales
Keywords
 Clifford analysis
 Fourier analysis
 signal processing
 singular integrals
 wavelets
Fields of Research
Code  Description  Percentage 

010106  Lie Groups, Harmonic and Fourier Analysis  75 
010399  Numerical and Computational Mathematics not elsewhere classified  15 
010499  Statistics not elsewhere classified  10 
Professional Experience
UON Appointment
Title  Organisation / Department 

Associate Professor  University of Newcastle School of Mathematical and Physical Sciences Australia 
Academic appointment
Dates  Title  Organisation / Department 

1/3/1985  1/7/1989  Tutor  The University of New South Wales School of Mathematical Sciences Australia 
1/7/2006  1/12/2008  Associate Professor  University of Arkansas Department of Mathematical Sciences United States 
1/8/2000  1/7/2006  Assistant Professor  University of Arkansas Department of Mathematical Sciences United States 
1/8/1989  1/8/1991  Lecturer  University of Texas At Austin Department of Mathematics United States 
1/9/1991  1/6/1993  Research Associate  Flinders University Australia 
15/7/1993  31/8/2000  Research Associate  MACCS, Macquarie University Australia 
Publications
For publications that are currently unpublished or inpress, details are shown in italics.
Book (7 outputs)
Year  Citation  Altmetrics  Link  

2013 
Hogan J, AMSI International Conference on Harmonic Analysis and Applications (Macquarie University, February 2011), Centre for Mathematics and its Applications, Mathematical Sciences Institute, the Australian National University, Canberra, 147 (2013)


2013 
Hogan J, AMSI International Conference on Harmonic Analysis and Applications (Macquarie University, February 2011), Centre for Mathematics and its Applications, Mathematical Sciences Institute, the Australian National University, Canberra, 147 (2013)


2012 
Hogan JA, Lakey JD, Duration and Bandwidth Limiting: Prolate Functions, Sampling, and Applications, Birkhauser, New York, 258 (2012) [A1]


2012  Hogan JA, Lakey JD, Preface (2012)  
2005 
Hogan JA, Lakey JD, Timefrequency and timescale methods: Adaptive decompositions, uncertainty principles, and sampling (2005) [A1]


2005  Hogan JA, Lakey JD, Preface (2005)  
2002 
Gilbert JE, Han YS, Hogan JA, Lakey JD, Weiland D, Weiss G, Smooth molecular decompositions of functions and singular integral operators (2002) [A1] Under minimal assumptions on a function ¿ we obtain wavelettype frames of the form ¿j,k(x) = r1/2nj¿(rjx  sk) j ¿ Z k ¿ Zn for some r > 1 and s > 0. This collection is show... [more] Under minimal assumptions on a function ¿ we obtain wavelettype frames of the form ¿j,k(x) = r1/2nj¿(rjx  sk) j ¿ Z k ¿ Zn for some r > 1 and s > 0. This collection is shown to be a frame for a scale of TriebelLizorkin spaces (which includes Lebesgue, Sobolev and Hardy spaces) and the reproducing formula converges in norm as well as pointwise a.e. The construction follows from a characterization of those operators which are bounded on a space of smooth molecules. This characterization also allows us to decompose a broad range of singular integral operators in terms of smooth molecules.


Show 4 more books 
Chapter (16 outputs)
Year  Citation  Altmetrics  Link  

2020 
Hogan JA, Lakey JD, 'Prolate Shift Frames and Sampling of Bandlimited Functions', Sampling: Theory and Applications A Centennial Celebration of Claude Shannon, Birkhäuser, Cham, Switzerland 141167 (2020) [B1]


2017 
Hogan JA, Lakey JD, 'Frame properties of shifts of prolate and bandpass prolate functions', Frames and other bases in abstract and function spaces. Novel Methods in Harmonic Analysis, Birkhauser Basel, New York 215235 (2017) [B1]


2012  Hogan JA, Morris AJ, 'Translationinvariant Clifford operators', , Australian National University 48 (2012) [E3]  
2012 
Hogan JA, Lakey JD, 'Thomson s multitaper method and applications to channel modeling', Applied and Numerical Harmonic Analysis 91127 (2012) © Springer Science+Business Media, LLC 2012. One of the most basic applications of Fourier analysis is power spectrum estimation. Some historical comments on this ageold problem ... [more] © Springer Science+Business Media, LLC 2012. One of the most basic applications of Fourier analysis is power spectrum estimation. Some historical comments on this ageold problem can be found in review articles by Robinson [279] and Benedetto [23], and in Percival and Walden¿s book [264]. We refer to Appendix A for basic definitions and properties, and references for stochastic processes. In the problem of estimating a widesense stationary random process from data, one has only finitely many samples, often of a single realization of the process, with which to work.


2012 
Hogan JA, Lakey JD, 'Timelocalized sampling approximations', Applied and Numerical Harmonic Analysis 199221 (2012) © Springer Science+Business Media, LLC 2012. In this last chapter we explore briefly some connections among sampling and time and band limiting. The chapter begins by pointing out... [more] © Springer Science+Business Media, LLC 2012. In this last chapter we explore briefly some connections among sampling and time and band limiting. The chapter begins by pointing out a general connection between the samples of eigenfunctions of time and band limiting and the eigenvectors of a certain matrix whose entries are, in essence, the samples of timelocalized images of functions that interpolate the samples in the given Paley¿Wiener space. Next, a discrete method is considered for generating eigenfunctions of time¿frequency localizations to unions of sets from their separate localizations. We then reconsider the connection between eigenfunctions and their samples in the concrete context of localization to intervals of the real line, outlining work ofWalter and Shen [347] and of Khare and George [177].Walter and Shen provided L2estimates for approximate prolate spheroidal wave functions (PSWFs) constructed from interpolation of their sample values within the timelocalization interval. We provide a partial sharpening of their estimates by using a slightly enlarged set of samples.


2012 
Hogan JA, Lakey JD, 'Time and band limiting of multiband signals', Applied and Numerical Harmonic Analysis 129151 (2012) © Springer Science+Business Media, LLC 2012. When a = 2OT, the operator POQT corresponding to single time and frequency intervals has an eigenvalue ¿¿a¿¿1/2, as Theorem 4.1.2 belo... [more] © Springer Science+Business Media, LLC 2012. When a = 2OT, the operator POQT corresponding to single time and frequency intervals has an eigenvalue ¿¿a¿¿1/2, as Theorem 4.1.2 belowwill show. The norm ¿0(a = 1) of the operator PQ1/2 satisfies ¿0(a = 1) = ¿sinc 1[1/2,1/2]¿ > 0.88. The trace of PQ1/2 is equal to a = 1, on the one hand and to S¿n on the other, so ¿1(a = 1) = 1¿0(a = 1) < 1/2. Suppose that T = 1 and S is a finite, pairwise disjoint union of a frequency intervals I1, ¿, Ia each of unit length. Then PSQ should have on the order of a eigenvalues of magnitude at least 1/2. Consider now the limiting case in which the frequency intervals become separated at infinity. Any function ¿j that is concentrated in frequency on Ij will be almost orthogonal over [T,T], in the separation limit, to any function ¿k that is frequencyconcentrated on Ik when j ¿ k.


2012 
Hogan JA, Lakey JD, 'Sampling of bandlimited and multiband signals', Applied and Numerical Harmonic Analysis 153198 (2012) © Springer Science+Business Media, LLC 2012. We provide here an overview of sampling theory that emphasizes realvariable aspects and functional analytic methods rather than analy... [more] © Springer Science+Business Media, LLC 2012. We provide here an overview of sampling theory that emphasizes realvariable aspects and functional analytic methods rather than analytic functiontheoretic ones. While this approach does not justify the most powerful mathematical results, it does provide the basis for practical sampling techniques for bandlimited and multiband signals.


2012 
Hogan JA, Lakey JD, 'Numerical aspects of time and band limiting', Applied and Numerical Harmonic Analysis 4590 (2012) © Springer Science+Business Media, LLC 2012. This chapter is concerned with the role of the prolates in numerical analysis¿ particularly their approximation properties and applica... [more] © Springer Science+Business Media, LLC 2012. This chapter is concerned with the role of the prolates in numerical analysis¿ particularly their approximation properties and application in the numerical solution of differential equations. The utility of the prolates in these contexts is due principally to the fact that they form a Markov system (see Defn. 2.1.6) of functions on [11], a property that stems from their status as eigenfunctions of the differential operator P of (1.6), and allows the full force of the Sturm¿Liouville theory to be applied. The Markov property immediately gives the orthogonality of the prolates on [11] (previously observed in Sect. 1.2 as the double orthogonality property) and also a remarkable collection of results regarding the zeros of the prolates as well as quadrature properties that are central to applications in numerical analysis.


2012 
Hogan JA, Lakey JD, 'The bell labs theory', Applied and Numerical Harmonic Analysis 143 (2012) © Springer Science+Business Media, LLC 2012. Duration limiting, or time limiting, refers to restricting a signal by setting its values equal to zero outside of a finite time inter... [more] © Springer Science+Business Media, LLC 2012. Duration limiting, or time limiting, refers to restricting a signal by setting its values equal to zero outside of a finite time interval or, more generally, outside of a compact set. Bandwidth limiting, or band limiting, refers to restricting a signal by setting its amplitudes equal to zero outside of a finite frequency interval or again, more generally, outside of a compact set. This book addresses primarily the theory of time and band limiting whose core was developed by Landau, Pollak, and Slepian in a series of papers [195, 196, 303, 309] appearing in the Bell System Technical Journal in the early to middle part of the 1960s, and a broader body of work that grew slowly but steadily out of that core up until around 1980, with a resurgence since 2000, due in large part to the importance of time and band limiting in wireless communications. The 1960s Bell Labs theory of time and band limiting is but one aspect of the Bell Labs information theory. The foundations of this encompassing theory were laid, in large part, in Nyquist¿s fundamental papers ¿Certain Topics in Telegraph Transmission Theory¿ [247], which appeared in the Transactions of the American Institute of Electrical Engineers in 1928, and ¿Certain Factors Affecting Telegraph Speed,¿ published in April 1924 in the Bell System Technical Journal, along with Hartley¿s paper ¿Transmission of Information,¿ which also appeared in the Bell System Technical Journal in 1928 [137]. These papers quantified general ideas that were in the air, though certain specific versions were attributed to Kelvin and Wiener among others. Of course, Claude Shannon¿s seminal work, ¿A Mathematical Theory of Communication,¿ which appeared in the Bell System Technical Journal in July and October 1948 [293], is often cited as providing the basis for much of modern communications theory. His sampling theory plays a central role in Chap. 5 of this monograph. The works of Nyquist and Hartley however remain, in some ways, more germane to the study at hand.


2008 
Hogan JA, Lakey JD, 'Sampling and timefrequency localization of bandlimited and multiband signals', Applied and Numerical Harmonic Analysis 275291 (2008) [B1] © 2008, Birkhäuser Boston. This chapter develops aspects of previous work ([10] and [11]) that pertain distinctly to bandlimited functions. In particular, we discuss some represe... [more] © 2008, Birkhäuser Boston. This chapter develops aspects of previous work ([10] and [11]) that pertain distinctly to bandlimited functions. In particular, we discuss some representation formulas for bandlimited functions in terms of periodic nonuniform samples. In the case of multiband signals, periodic nonuniform sampling is often valid at a lower sampling rate than is uniform sampling, as will be discussed. Finally, we will consider some related questions about optimally time and multibandlimited signals.


2006 
Hogan JA, Lakey JD, 'Periodic Nonuniform Sampling in ShiftInvariant Spaces', Applied and Numerical Harmonic Analysis 253287 (2006) [B1] © 2006, Birkhäuser Boston. This chapter reviews several ideas that grew out of observations of Djokovic and Vaidyanathan to the effect that a generalized sampling method for bandl... [more] © 2006, Birkhäuser Boston. This chapter reviews several ideas that grew out of observations of Djokovic and Vaidyanathan to the effect that a generalized sampling method for bandlimited functions, due to Papoulis, could be carried over in many cases to the spline spaces and other shiftinvariant spaces. Papoulis¿ method is based on the sampling output of linear, timeinvariant systems. Unser and Zerubia formalized Papoulis¿ approach in the context of shiftinvariant spaces. However, it is not easy to provide useful conditions under which the UnserZerubia criterion provides convergent and stable sampling expansions. Here we review several methods for validating the UnserZerubia approach for periodic nonuniform sampling, which is a very special case of generalized sampling. The Zak transform plays an important role.


Show 13 more chapters 
Journal article (28 outputs)
Year  Citation  Altmetrics  Link  

2019 
Hogan JA, Lakey JD, 'An Analogue of Slepian Vectors on Boolean Hypercubes', Journal of Fourier Analysis and Applications, 25 20042020 (2019) [C1]


2019 
Hogan JA, Massopust PR, 'Quaternionic Fundamental Cardinal Splines: Interpolation and Sampling', Complex Analysis and Operator Theory, 13 33733403 (2019) [C1]


2017 
Hogan JA, Massopust P, 'Quaternionic Bsplines', Journal of Approximation Theory, 224 4365 (2017) [C1]


2017 
Franklin DJ, Hogan JA, Larkin KG, 'Hardy, PaleyWiener and Bernstein spaces in Clifford analysis', COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 62 13141328 (2017) [C1]


2017 
Hogan JA, Lakey JD, 'On the Numerical Evaluation of Bandpass Prolates II', JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 23 125140 (2017) [C1]


2016 
Hogan JA, Lakey JD, 'Frame expansions of bandlimited signals using prolate spheroidal wave functions', Sampling Theory in Signal and Image Processing, 15 139153 (2016) [C1] © 2016 SAMPLING PUBLISHING. We consider methods to compute duals of frames for Paley¿Wiener spaces generated by shifts of certain prolate spheroidal wave functions. In particular,... [more] © 2016 SAMPLING PUBLISHING. We consider methods to compute duals of frames for Paley¿Wiener spaces generated by shifts of certain prolate spheroidal wave functions. In particular, we consider methods to compute frame expansions restricted to subbandlimited functions. Methods to compute dual frame generators are also provided in the case of corresponding frames for spaces of bandpasslimited signals.


2015 
Hogan JA, Lakey JD, 'Frame properties of shifts of prolate spheroidal wave functions', Applied and Computational Harmonic Analysis, 39 2132 (2015) [C1] © 2014 Elsevier Inc. Abstract We provide conditions on a shift parameter and number of basic prolate spheroidal wave functions with a fixed bandwidth and time concentrated to a fi... [more] © 2014 Elsevier Inc. Abstract We provide conditions on a shift parameter and number of basic prolate spheroidal wave functions with a fixed bandwidth and time concentrated to a fixed duration such that the shifts of the basic prolates form a frame or a Riesz basis for the PaleyWiener space consisting of all square integrable functions with the given bandlimit.


2014 
Ogburn DX, Waters CL, Sciffer MD, Hogan JA, Abbott PC, 'A finite difference construction of the spheroidal wave functions', COMPUTER PHYSICS COMMUNICATIONS, 185 244253 (2014) [C1]


2014 
Hogan JA, Kroger J, Lakey JD, 'Time and bandpass limiting and an application to EEG', Sampling Theory in Signal and Image Processing, 13 295313 (2014) [C1]


2013 
Craddock MJ, Hogan JA, 'The Fractional CliffordFourier Kernel', JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 19 683711 (2013) [C1]


2013 
Hogan JA, Lakey JD, 'Letter to the Editor: On the Numerical Evaluation of Bandpass Prolates', Journal of Fourier Analysis and Applications, 19 439446 (2013) [C1] This letter provides a technique for numerical evaluation of certain eigenfunctions of the integral kernel operator corresponding to time truncation of a squareintegrable functio... [more] This letter provides a technique for numerical evaluation of certain eigenfunctions of the integral kernel operator corresponding to time truncation of a squareintegrable function to a finite interval, followed by frequency limiting to frequencies in an annular band. © 2013 Springer Science+Business Media New York.


2012 
Hogan JA, Morris AJ, 'Quaternionic wavelets', Numerical Functional Analysis and Optimization, 33 10311062 (2012) [C1]


2012 
Lakey JD, Hogan JA, 'On the numerical computation of certain eigenfunctions of time and multiband limiting', Numerical Functional Analysis and Optimization, 33 10951111 (2012) [C1]


2010 
Hogan JA, Izu S, Lakey JD, 'Sampling approximations for time and bandlimiting', Sampling Theory in Signal and Image Processing, 9 91117 (2010) [C1]


2009 
Hogan JA, Lakey J, 'Nontranslationinvariance and the synchronization problem in wavelet sampling', Acta Applicandae Mathematicae, 107 373398 (2009) [C1]


2006 
Hogan JA, Lakey JD, 'On uncertainty bounds and growth estimates for fractional Fourier transforms', Applicable Analysis, 85 891899 (2006) [C1] Gelfand¿Shilov spaces are spaces of entire functions defined in terms of a rate of growth in one direction and a concomitant rate of decay in an orthogonal direction. Gelfand and ... [more] Gelfand¿Shilov spaces are spaces of entire functions defined in terms of a rate of growth in one direction and a concomitant rate of decay in an orthogonal direction. Gelfand and Shilov proved that the Fourier transform is an isomorphism among certain of these spaces. In this article we consider mapping properties of fractional Fourier transforms on Gelfand¿Shilov spaces. Just as the Fourier transform corresponds to rotation through a right angle in the phase plane, fractional Fourier transforms correspond to rotations through intermediate angles. Therefore, the aim of fractional Fourier estimates is to set up a correspondence between growth properties in the complex plane versus decay properties in phase space. © 2006, Taylor & Francis Group, LLC.


2006 
Hogan JA, Lakey JD, 'Hardy's theorem and rotations', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 134 14591466 (2006) [C1]


2005 
Hogan JA, Lakey JD, 'Sampling and oversampling in shiftinvariant and multiresolution spaces 1: Validation of sampling schemes', INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 3 257281 (2005) [C1]


2005 
Gilbert JE, Hogan JA, Lakey JD, 'BMO, boundedness of affine operators, and frames', APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 18 324 (2005) [C1]


2002 
Gilbert JE, Han YS, Hogan JA, Lakey JD, Weiland D, Weiss G, 'Smooth molecular decompositions of functions and singular integral operators', Memoirs of the American Mathematical Society, (2002) Under minimal assumptions on a function ¿ we obtain wavelettype frames of the form ¿j,k(x) = r1/2nj¿(rjx  sk) j ¿ Z k ¿ Zn for some r > 1 and s > 0. This collection is show... [more] Under minimal assumptions on a function ¿ we obtain wavelettype frames of the form ¿j,k(x) = r1/2nj¿(rjx  sk) j ¿ Z k ¿ Zn for some r > 1 and s > 0. This collection is shown to be a frame for a scale of TriebelLizorkin spaces (which includes Lebesgue, Sobolev and Hardy spaces) and the reproducing formula converges in norm as well as pointwise a.e. The construction follows from a characterization of those operators which are bounded on a space of smooth molecules. This characterization also allows us to decompose a broad range of singular integral operators in terms of smooth molecules.


2000 
Gilbert JE, Hogan JA, Lakey JD, 'Characterization of Hardy spaces by singular integrals and 'divergencefree' wavelets', PACIFIC JOURNAL OF MATHEMATICS, 193 79105 (2000)


2000 
Hogan J, Li C, McIntosh A, Zhang K, 'Global higher integrability of Jacobians on bounded domains', Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 17 193217 (2000) We give conditions for a vectorvalued function u ¿ W1,n (O, Rn), satisfying det Du (x) 0 on a bounded domain O, which imply that det Du (x) is globally higher integrable on O. We... [more] We give conditions for a vectorvalued function u ¿ W1,n (O, Rn), satisfying det Du (x) 0 on a bounded domain O, which imply that det Du (x) is globally higher integrable on O. We also give conditions for u ¿ W1,n (O, Rn) such that det Du belongs to the Hardy space h1z (O) and exhibit some examples which show that our conditions are in some sense optimal. Applications to the weak convergence of Jacobians follow. Divcurl type extensions of these results to forms are also considered. © 2000 Editions scientifiques et médicales Elsevier SAS.


Show 25 more journal articles 
Conference (17 outputs)
Year  Citation  Altmetrics  Link  

2019 
Ghaffari HB, Hogan JA, Lakey JD, 'A Clifford Construction of Multidimensional Prolate Spheroidal Wave Functions', 2019 13th International Conference on Sampling Theory and Applications, SampTA 2019, Bordeaux, France (2019) [E1]


2019 
Franklin D, Hogan JA, Tam M, 'Higherdimensional wavelets and the DouglasRachford algorithm', 2019 13th International Conference on Sampling Theory and Applications, SampTA 2019, Bordeaux, France (2019) [E1]


2019 
Hogan JA, Lakey JD, 'Numerical computation of eigenspaces of spatiospectral limiting on hypercubes', 2019 13th International Conference on Sampling Theory and Applications, SampTA 2019, Bordeaux, France (2019) [E1]


2019 
Dizon ND, Hogan JA, Lakey JD, 'Optimization in the construction of nearly cardinal and nearly symmetric wavelets', 2019 13th International Conference on Sampling Theory and Applications, SampTA 2019, Bordeaux, France (2019) [E1]


2017  Hogan JA, Lakey J, 'Sampling in PaleyWiener spaces, uncertainty and the prolate spheroidal wavefunctions', Proceedings of the AMSI/AustMS 2014 Workshop in Harmonic Analysis and its Applications, Sydney, Australia (2017) [E1]  
2017 
Hogan JA, Lakey JD, 'Riesz bounds for prolate shifts', 2017 INTERNATIONAL CONFERENCE ON SAMPLING THEORY AND APPLICATIONS (SAMPTA), Tallinn, ESTONIA (2017) [E1]


2017  Hogan JA, Lakey JD, 'Bandpass pseudo prolate shift frames and Riesz bases', 2017 INTERNATIONAL CONFERENCE ON SAMPLING THEORY AND APPLICATIONS (SAMPTA), Tallinn, ESTONIA (2017) [E1]  
2015 
Hogan JA, Lakey JD, 'Prolate shift frames and their duals', 2015 International Conference on Sampling Theory and Applications, SampTA 2015, Washington, DC (2015) [E1]


2015 
Hogan JA, Lakey JD, 'Wavelet frames generated by bandpass prolate functions', 2015 International Conference on Sampling Theory and Applications, SampTA 2015 (2015) [E1] © 2015 IEEE. We refer to eigenfunctions of the kernel corresponding to truncation in a time interval followed by truncation in a frequency band as bandpass prelates (BPPs). We pro... [more] © 2015 IEEE. We refer to eigenfunctions of the kernel corresponding to truncation in a time interval followed by truncation in a frequency band as bandpass prelates (BPPs). We prove frame bounds for certain families of shifts of bandpass prolates, and we numerically construct dual frames for finite dimensional analogues. In the continuous case, the corresponding families produce wavelet frames for the space of squareintegrable functions.


2013  Hogan JA, Lakey JD, 'Sampling aspects of approximately timelimited multiband and bandpass signals', Proceedings of the 10th International Conference on Sampling Theory and Applications (SampTA 2013), Bremen, Germany (2013) [E1]  
2000 
Hogan JA, Lakey J, 'Sampling for shiftinvariant and wavelet subspaces', WAVELET APPLICATIONS IN SIGNAL AND IMAGE PROCESSING VIII PTS 1 AND 2, SAN DIEGO, CA (2000)


Show 14 more conferences 
Grants and Funding
Summary
Number of grants  6 

Total funding  $1,143,589 
Click on a grant title below to expand the full details for that specific grant.
20201 grants / $527,468
Enhanced Fractionation of Mineral Particles According to Density$527,468
Funding body: ARC (Australian Research Council)
Funding body  ARC (Australian Research Council) 

Project Team  Laureate Professor Kevin Galvin, Associate Professor Jeffrey Hogan 
Scheme  Discovery Projects 
Role  Investigator 
Funding Start  2020 
Funding Finish  2022 
GNo  G1900136 
Type Of Funding  Aust Competitive  Commonwealth 
Category  1CS 
UON  Y 
20171 grants / $13,500
Multichannel Image and Signal Analysis: Phase and Geometry$13,500
Funding body: Bayerische Forschunsallianz
Funding body  Bayerische Forschunsallianz 

Project Team  Prof. Brigitte Forster, Dr Jeffrey Hogan, Dr Peter Massopust 
Scheme  Bayerischen Hochshulforderprogramms zur Ahnbahnung und Vertiefung internationaler Forschnungskooperationen 
Role  Investigator 
Funding Start  2017 
Funding Finish  2017 
GNo  
Type Of Funding  International  Competitive 
Category  3IFA 
UON  N 
20161 grants / $593,621
Relaxed reflection methods for feasibility and matrix completion problems$593,621
Funding body: ARC (Australian Research Council)
Funding body  ARC (Australian Research Council) 

Project Team  Laureate Professor Jon Borwein, Associate Professor Jeffrey Hogan, Associate Professor Russell Luke, Associate Professor Brailey Sims 
Scheme  Discovery Projects 
Role  Lead 
Funding Start  2016 
Funding Finish  2018 
GNo  G1500027 
Type Of Funding  Aust Competitive  Commonwealth 
Category  1CS 
UON  Y 
20141 grants / $2,000
Faculty PVC Conference Assistance Grant 2014$2,000
Funding body: University of Newcastle  Faculty of Science & IT
Funding body  University of Newcastle  Faculty of Science & IT 

Project Team  Associate Professor Jeffrey Hogan 
Scheme  PVC Conference Assistance Grant 
Role  Lead 
Funding Start  2014 
Funding Finish  2014 
GNo  G1401195 
Type Of Funding  Internal 
Category  INTE 
UON  Y 
20131 grants / $2,000
Faculty PVC Conference Assistance Grant 2013$2,000
Funding body: University of Newcastle  Faculty of Science & IT
Funding body  University of Newcastle  Faculty of Science & IT 

Project Team  Associate Professor Jeffrey Hogan 
Scheme  PVC Conference Assistance Grant 
Role  Lead 
Funding Start  2013 
Funding Finish  2013 
GNo  G1401161 
Type Of Funding  Internal 
Category  INTE 
UON  Y 
20101 grants / $5,000
Hypercomplex Signal Processing$5,000
Funding body: University of Newcastle
Funding body  University of Newcastle 

Project Team  Associate Professor Jeffrey Hogan 
Scheme  New Staff Grant 
Role  Lead 
Funding Start  2010 
Funding Finish  2010 
GNo  G1000074 
Type Of Funding  Internal 
Category  INTE 
UON  Y 
Research Supervision
Number of supervisions
Current Supervision
Commenced  Level of Study  Research Title  Program  Supervisor Type 

2018  PhD  Higherdimensional Prolate Spheroidal Wave Functions  PhD (Mathematics), Faculty of Science, The University of Newcastle  Principal Supervisor 
2017  PhD  Optimisation in the Construction of Multidimensional Wavelets  PhD (Mathematics), Faculty of Science, The University of Newcastle  Principal Supervisor 
2016  PhD  An Exploration of Generalised Convexity on Semigroups and Semimodules  PhD (Mathematics), Faculty of Science, The University of Newcastle  Principal Supervisor 
Past Supervision
Year  Level of Study  Research Title  Program  Supervisor Type 

2019  PhD  Forecasting in Supply Chains: The Impact of Demand Volatility in the Presence of Promotions  PhD (Statistics), Faculty of Science, The University of Newcastle  CoSupervisor 
2018  PhD  Projection Algorithms for Nonseparable Wavelets and Clifford Fourier Analysis  PhD (Mathematics), Faculty of Science, The University of Newcastle  Principal Supervisor 
2018  PhD  Random Walks On Groups  PhD (Mathematics), Faculty of Science, The University of Newcastle  CoSupervisor 
2014  PhD  Fourier and Wavelet Analysis of CliffordValued Functions  PhD (Mathematics), Faculty of Science, The University of Newcastle  Principal Supervisor 
Research Projects
Prolate functions : bandlimited and bandpass signal processing 2009 
Prolate functions have maximal energy concentration among all signals of a fixed bandlimit and have found many applications in signal processing, especially as taper functions for spectral estimation algorithms. This is due to their ``spectral accumulation'' properties. In this project, we
 construct bandpass prolates whose spectra are supported on a union of intervals on the line.
 construct prolate functions on graphs.
 develop the required aspects of Clifford analysis to enable the construction of bandlimited and bandpass prolates in higher dimensions.
Publications
Hogan JA, Lakey JD, Timefrequency and timescale methods: Adaptive decompositions, uncertainty principles, and sampling (2005) [A1]
Hogan JA, Lakey JD, 'Sampling and timefrequency localization of bandlimited and multiband signals', Applied and Numerical Harmonic Analysis 275291 (2008) [B1]
Hogan JA, Lakey JD, Duration and Bandwidth Limiting: Prolate Functions, Sampling, and Applications, Birkhauser, New York, 258 (2012) [A1]
Hogan JA, Lakey JD, 'Numerical aspects of time and band limiting', Applied and Numerical Harmonic Analysis 4590 (2012)
Lakey JD, Hogan JA, 'On the numerical computation of certain eigenfunctions of time and multiband limiting', Numerical Functional Analysis and Optimization, 33 10951111 (2012) [C1]
Hogan JA, Lakey JD, 'Timelocalized sampling approximations', Applied and Numerical Harmonic Analysis 199221 (2012)
Hogan JA, Lakey JD, 'Letter to the Editor: On the Numerical Evaluation of Bandpass Prolates', Journal of Fourier Analysis and Applications, 19 439446 (2013) [C1]
Hogan JA, Kroger J, Lakey JD, 'Time and bandpass limiting and an application to EEG', Sampling Theory in Signal and Image Processing, 13 295313 (2014) [C1]
Hogan JA, Lakey JD, 'Frame properties of shifts of prolate spheroidal wave functions', Applied and Computational Harmonic Analysis, 39 2132 (2015) [C1]
Hogan JA, Lakey JD, 'Prolate shift frames and their duals', 2015 International Conference on Sampling Theory and Applications, SampTA 2015, Washington, DC (2015) [E1]
Hogan JA, Lakey JD, 'Wavelet frames generated by bandpass prolate functions', 2015 International Conference on Sampling Theory and Applications, SampTA 2015 (2015) [E1]
Hogan JA, Lakey JD, 'Frame expansions of bandlimited signals using prolate spheroidal wave functions', Sampling Theory in Signal and Image Processing, 15 139153 (2016) [C1]
Hogan JA, Lakey JD, 'Bandpass pseudo prolate shift frames and Riesz bases', 2017 INTERNATIONAL CONFERENCE ON SAMPLING THEORY AND APPLICATIONS (SAMPTA), Tallinn, ESTONIA (2017) [E1]
Hogan JA, Lakey JD, 'Frame properties of shifts of prolate and bandpass prolate functions', Frames and other bases in abstract and function spaces. Novel Methods in Harmonic Analysis, Birkhauser Basel, New York 215235 (2017) [B1]
Hogan JA, Lakey JD, 'On the Numerical Evaluation of Bandpass Prolates II', JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 23 125140 (2017) [C1]
Hogan JA, Lakey JD, 'Riesz bounds for prolate shifts', 2017 INTERNATIONAL CONFERENCE ON SAMPLING THEORY AND APPLICATIONS (SAMPTA), Tallinn, ESTONIA (2017) [E1]
Students
Program  Research Title 

PhD Faculty of Science 
Higherdimensional Prolate Spheroidal Wave Functions 
Collaborators
Name  Organisation 

Joseph Lakey  New Mexico State University, Las Cruces 
Multidimensional wavelets 2016 
Among modern signal processing techniques, wavelets have provided the most important theoretical challenges and technological advances. The by now classical construction methods on the line require techniques from complex analysis that are not available in higher dimensions. In this project, we apply modern techniques of optimisation to the notoriously difficult construction of wavelets in two and higher dimensions. Outputs include:
 Wavelets on the line with improved properties (nearcardinality, nearsymmetry, etc).
 Wavelets on the plane with prescribed regularity.
With a view to applications in the processing of colour images, the team is working towards the development of quaternionvalued wavelets on the plane.
Grants
Relaxed reflection methods for feasibility and matrix completion problems
Funding body: ARC (Australian Research Council)
Funding body  ARC (Australian Research Council) 

Project Team  Laureate Professor Jon Borwein, Associate Professor Jeffrey Hogan, Associate Professor Russell Luke, Associate Professor Brailey Sims 
Scheme  Discovery Projects 
Publications
Hogan JA, Morris AJ, 'Quaternionic wavelets', Numerical Functional Analysis and Optimization, 33 10311062 (2012) [C1]
Franklin D, Hogan JA, Tam M, 'Higherdimensional wavelets and the DouglasRachford algorithm', 2019 13th International Conference on Sampling Theory and Applications, SampTA 2019, Bordeaux, France (2019) [E1]
Students
Program  Research Title 

PhD Faculty of Science 
Optimisation in the Construction of Multidimensional Wavelets 
Clifford splines 2012 
Spline functions are important components in signal processing algorithms  they are often used in finite element algorithms for the solution of differential equations and are also used in the smoothing of discrete data in computer graphics. In this project we investigate the application of Cliffordanalytic techniques to the construction of multichannel, multivariate splines appropriate to the treatment of multichannel signals such as colour images and video.
Grants
Multichannel Image and Signal Analysis: Phase and Geometry
Funding body: Bayerische Forschunsallianz
Funding body  Bayerische Forschunsallianz 

Description  For research visits between the participants to work on current research in which methods of Clifford analysis are applied to problems of multidimensional, multichannel signal and image analysis. 
Scheme  Bayerischen Hochshulforderprogramms zur Ahnbahnung und Vertiefung internationaler Forschnungskooperationen 
Publications
Hogan JA, Massopust P, 'Quaternionic Bsplines', Journal of Approximation Theory, 224 4365 (2017) [C1]
Hogan JA, Massopust PR, 'Quaternionic Fundamental Cardinal Splines: Interpolation and Sampling', Complex Analysis and Operator Theory, 13 33733403 (2019) [C1]
Collaborators
Name  Organisation 

Peter Massopust  Technical University of Munish 
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Research Collaborations
The map is a representation of a researchers coauthorship with collaborators across the globe. The map displays the number of publications against a country, where there is at least one coauthor based in that country. Data is sourced from the University of Newcastle research publication management system (NURO) and may not fully represent the authors complete body of work.
Country  Count of Publications  

United States  43  
Australia  41  
Germany  3  
Canada  1 
News
ARC Discovery Projects funding success
November 4, 2015
Associate Professor Jeffrey Hogan
Position
Associate Professor
School of Mathematical and Physical Sciences
Faculty of Science
Focus area
Mathematics
Contact Details
jeff.hogan@newcastle.edu.au  
Phone  (02) 4921 7235 
Fax  (02) 4921 6898 
Office
Room  SR243 

Building  Mathematics Building 
Location  Callaghan University Drive Callaghan, NSW 2308 Australia 