A Functional Analytic View on Time-Frequency Analysis

Time-Frequency Analysis is a fertile branch of mathematical analysis, centered around the Short-Time Fourier Transform. Specifically, Gabor Analysis is concerned with studies of the sampled STFT, resp. atomic (non-orthogonal) representations of distributions using TF-shifted copies of a Gabor atom. In these studies a family of Banach spaces of distributions, the so-called Modulation Spaces, play an important role, in order to describe the continuity of relevant operators, possible classes of atoms, the various symbols connected with linear operators (including pseudo-differential operators), or the behaviour of so-called Gabor multipliers.

Hans Feichtinger

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