Rate My Professor Jeffrey Hogan

Hogan's research specializes in pure, applied, and computational harmonic analysis, encompassing uncertainty principles for the Fourier transform on locally compact groups, singular integrals and wavelet frames, sampling theory in Fourier and wavelet analysis, Clifford-Fourier theory, bandlimited and bandpass prolate functions in one and higher dimensions, applications of optimisation in constructing one- and multi-dimensional wavelets, and fractionation of minerals according to size and density. Key fields include Lie groups, harmonic and Fourier analysis (60%), approximation theory and asymptotic methods (30%), and signal processing (10%). Notable publications include 'Duration and Bandwidth Limiting: Prolate Functions, Sampling, and Applications' (2012, with J.D. Lakey), 'Time-frequency and time-scale methods: adaptive decompositions, uncertainty principles, and sampling' (2005, with J.D. Lakey), 'Smooth Molecular Decompositions of Functions and Singular Integral Operators' (2002, with J.E. Gilbert et al.), 'Quaternionic B-splines' (2017, with P. Massopust), and 'Prolate Shift Frames and Sampling of Bandlimited Functions' (2020, with J.D. Lakey). He has secured grants totaling $1,163,034, including ARC Discovery Projects on enhanced fractionation of mineral particles (2020, $546,913) and relaxed reflection methods for feasibility problems (2016, $593,621). Hogan has supervised eight completions, including PhDs on metric projections, higher-dimensional prolate functions, and multidimensional wavelets, and collaborates with researchers such as Laureate Professor Kevin Galvin and Professor Joseph Lakey.