Dr Jeffrey Hogan

© 2017 Informa UK Limited, trading as Taylor & Francis Group. We describe the relationship between the growth conditions of monogenic extensions of square-integrable functions f in terms of pointwise bounds or bounds on integral averages on the one hand, and the support of the Fourier transform f or its annihilation by certain higher-dimensional analogues of the signum function on the other. We review known results involving a function¿s monogenic extension and their classical Fourier transform. These results are extended to the Clifford-Fourier transform of Brackx, De Schepper and Sommen. The equivalence of the pointwise bounds and the bounds on the integral averages is observed as a consequence.

© 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.

© 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.