Dr Jeffrey Hogan
Senior Lecturer
School of Mathematical and Physical Sciences (Mathematics)
- Email:jeff.hogan@newcastle.edu.au
- Phone:(02) 4921 7235
Career Summary
Biography
Harmonic analysis: wavelets; frames; singular integrals; Fourier analysis; signal processing; time-frequency analysis; Clifford analysis; uncertainty principles; fractional Fourier transforms; sampling; analysis on the Heisenberg group.
Qualifications
- PhD, University of New South Wales
- Bachelor of Science, University of New South Wales
Keywords
- wavelets
- Fourier analysis
- Clifford analysis
- signal processing
- singular integrals
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 |
|---|---|
| Senior Lecturer | University of Newcastle School of Mathematical and Physical Sciences Australia |
Academic appointment
| Dates | Title | Organisation / Department |
|---|---|---|
| 1/07/2006 - 1/12/2008 | Associate Professor | University of Arkansas Department of Mathematical Sciences United States |
| 1/08/2000 - 1/07/2006 | Assistant Professor | University of Arkansas Department of Mathematical Sciences United States |
| 1/09/1991 - 1/06/1993 | Research Associate | Flinders University Australia |
| 1/08/1989 - 1/08/1991 | Lecturer | University of Texas At Austin Department of Mathematics United States |
| 1/03/1985 - 1/07/1989 | Tutor | The University of New South Wales School of Mathematical Sciences Australia |
Publications
For publications that are currently unpublished or in-press, details are shown in italics.
Book (5 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]
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Chapter (7 outputs)
| Year | Citation | Altmetrics | Link |
|---|---|---|---|
| 2012 | Hogan JA, Morris AJ, 'Translation-invariant Clifford operators', , Australian National University 48 (2012) [E3] | ||
| 2008 | Hogan J, Lakey JD, 'Sampling and Time-Frequency Localization of Band-Limited and Multiband Signals', Representations, wavelets and frames : a celebration of the mathematical work of Lawrence Baggett, Springer, Berlin, Germany 275-292 (2008) [B1] | ||
| 2006 | Hogan J, Lakey JD, 'Periodic Nonuniform Sampling in Shift-Invariant Spaces', Harmonic Analysis and Applications : In Honor of John J. Benedetto, Birkhauser, Basel, Switzerland 253-286 (2006) [B1] | ||
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Journal article (25 outputs)
| Year | Citation | Altmetrics | Link | ||||||||
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| 2017 |
Hogan JA, Massopust P, 'Quaternionic B-splines', Journal of Approximation Theory, 224 43-65 (2017) [C1]
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| 2017 |
Franklin DJ, Hogan JA, Larkin KG, 'Hardy, Paley-Wiener and Bernstein spaces in Clifford analysis', COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 62 1314-1328 (2017) [C1]
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| 2017 |
Hogan JA, Lakey JD, 'On the Numerical Evaluation of Bandpass Prolates II', JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 23 125-140 (2017)
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| 2016 |
Hogan JA, Lakey JD, 'Frame expansions of bandlimited signals using prolate spheroidal wave functions', Sampling Theory in Signal and Image Processing, 15 139-153 (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 subband-limited functions. Methods to compute dual frame generators are also provided in the case of corresponding frames for spaces of bandpass-limited signals. |
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| 2015 |
Hogan JA, Lakey JD, 'Frame properties of shifts of prolate spheroidal wave functions', Applied and Computational Harmonic Analysis, 39 21-32 (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 Paley-Wiener space consisting of all square integrable functions with the given bandlimit.
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| 2014 |
Ogburn DX, Waters CL, Sciffer MD, Hogan JA, Abbott PC, 'A finite difference construction of the spheroidal wave functions', COMPUTER PHYSICS COMMUNICATIONS, 185 244-253 (2014) [C1]
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| 2014 |
Hogan JA, Kroger J, Lakey JD, 'Time and bandpass limiting and an application to EEG', Sampling Theory in Signal and Image Processing, 13 295-313 (2014) [C1]
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| 2013 |
Craddock MJ, Hogan JA, 'The Fractional Clifford-Fourier Kernel', JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 19 683-711 (2013) [C1]
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| 2013 |
Hogan JA, Lakey JD, 'Letter to the Editor: On the Numerical Evaluation of Bandpass Prolates', Journal of Fourier Analysis and Applications, 19 439-446 (2013) [C1] This letter provides a technique for numerical evaluation of certain eigenfunctions of the integral kernel operator corresponding to time truncation of a square-integrable functio... [more] This letter provides a technique for numerical evaluation of certain eigenfunctions of the integral kernel operator corresponding to time truncation of a square-integrable function to a finite interval, followed by frequency limiting to frequencies in an annular band. © 2013 Springer Science+Business Media New York.
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| 2012 |
Hogan JA, Morris AJ, 'Quaternionic wavelets', Numerical Functional Analysis and Optimization, 33 1031-1062 (2012) [C1]
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| 2012 |
Lakey JD, Hogan JA, 'On the numerical computation of certain eigenfunctions of time and multiband limiting', Numerical Functional Analysis and Optimization, 33 1095-1111 (2012) [C1]
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| 2010 |
Hogan JA, Izu S, Lakey JD, 'Sampling approximations for time- and bandlimiting', Sampling Theory in Signal and Image Processing, 9 91-117 (2010) [C1]
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| 2009 |
Hogan JA, Lakey J, 'Non-translation-invariance and the synchronization problem in wavelet sampling', Acta Applicandae Mathematicae, 107 373-398 (2009) [C1]
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| 2006 |
Hogan JA, Lakey JD, 'Hardy's theorem and rotations', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 134 1459-1466 (2006) [C1]
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| 2005 |
Hogan JA, Lakey JD, 'Sampling and oversampling in shift-invariant and multiresolution spaces 1: Validation of sampling schemes', INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 3 257-281 (2005) [C1]
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| 2005 |
Gilbert JE, Hogan JA, Lakey JD, 'BMO, boundedness of affine operators, and frames', APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 18 3-24 (2005) [C1]
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| 2000 |
Gilbert JE, Hogan JA, Lakey JD, 'Characterization of Hardy spaces by singular integrals and 'divergence-free' wavelets', PACIFIC JOURNAL OF MATHEMATICS, 193 79-105 (2000)
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Conference (12 outputs)
| Year | Citation | Altmetrics | Link | |||||
|---|---|---|---|---|---|---|---|---|
| 2017 |
Hogan JA, Lakey JD, 'Bandpass pseudo prolate shift frames and Riesz bases', 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017 (2017) © 2017 IEEE. We investigate frames and Riesz bases for the space of square-integrable functions on the line whose Fourier transforms are supported on the union of two disjoint int... [more] © 2017 IEEE. We investigate frames and Riesz bases for the space of square-integrable functions on the line whose Fourier transforms are supported on the union of two disjoint intervals (bandpass signals). By suitably modulating a frame (resp. Riesz basis) for the Paley-Wiener space PW O which is generated by the shifts of prolate spheroidal wave functions, we generate frames (reps. Riesz bases) for the bandpass space, and show that the frame (resp. Riesz) bounds are the same as those of the baseband frame (resp. Riesz basis).
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| 2017 |
Hogan JA, Lakey JD, 'Riesz bounds for prolate shifts', 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017 (2017) © 2017 IEEE. We investigate shifts of prolate spheroidal wave functions and more particularly the shift-invariant spaces generated by the shifts of the first N of these functions.... [more] © 2017 IEEE. We investigate shifts of prolate spheroidal wave functions and more particularly the shift-invariant spaces generated by the shifts of the first N of these functions. The Markov property satisfied by the prolates is used to show that at the Nyquist rate, such collections form a Riesz basis for the associated Paley-Wiener space, although explicit Riesz bounds cannot be derived. The fact that the prolate functions are eigenfunctions of the finite Fourier transform and a quadrature estimate for integrals of complex exponentials is used to provide Riesz bounds when the sampling rate is much lower than Nyquist. In this case, the Riesz basis will typically not span all of the Paley-Wiener space.
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| 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]
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| 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 square-integrable functions.
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| 2013 | Hogan JA, Lakey JD, 'Sampling aspects of approximately time-limited 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 shift-invariant and wavelet subspaces', WAVELET APPLICATIONS IN SIGNAL AND IMAGE PROCESSING VIII PTS 1 AND 2, SAN DIEGO, CA (2000)
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Grants and Funding
Summary
| Number of grants | 4 |
|---|---|
| Total funding | $602,620 |
Click on a grant title below to expand the full details for that specific grant.
20161 grants / $593,620
Relaxed reflection methods for feasibility and matrix completion problems$593,620
Funding body: ARC (Australian Research Council)
| Funding body | ARC (Australian Research Council) |
|---|---|
| Project Team | Laureate Professor Jon Borwein, Doctor 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 | Doctor 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 | Doctor 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 | Doctor 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
Total current UON EFTSL
Current Supervision
| Commenced | Level of Study | Research Title | Program | Supervisor Type |
|---|---|---|---|---|
| 2018 | PhD | Higher-dimensional Prolate Spheroidal Wave Functions | PhD (Mathematics), Faculty of Science, The University of Newcastle | Principal Supervisor |
| 2017 | PhD | Optimization, Iterated Projections and the Douglas-Rachford Method 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 |
| 2014 | PhD | Projection Algorithms for Non-separable Wavelets and Clifford Fourier Analysis | PhD (Mathematics), Faculty of Science, The University of Newcastle | Principal Supervisor |
| 2014 | PhD | Random Walks On Groups | PhD (Mathematics), Faculty of Science, The University of Newcastle | Co-Supervisor |
Past Supervision
| Year | Level of Study | Research Title | Program | Supervisor Type |
|---|---|---|---|---|
| 2014 | PhD | Fourier and Wavelet Analysis of Clifford-Valued Functions | PhD (Mathematics), Faculty of Science, The University of Newcastle | Principal Supervisor |
Research Collaborations
The map is a representation of a researchers co-authorship with collaborators across the globe. The map displays the number of publications against a country, where there is at least one co-author 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 | 28 | |
| Australia | 24 | |
| Canada | 1 | |
| Germany | 1 |
News
ARC Discovery Projects funding success
November 4, 2015
Dr Jeffrey Hogan
Position
Senior Lecturer
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 | V128 |
|---|---|
| Building | Mathematics Building |
| Location | Callaghan University Drive Callaghan, NSW 2308 Australia |
NEWS • Nov 04.2015
ARC Discovery Projects funding success
Laureate Professor Jon Borwein, Dr Jeffrey Hogan and Professor Dr Russell Luke have been awarded more than $560,000 in ARC Discovery Project funding commenc
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