**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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