Since its invention in 1979 the Feichtinger algebra has become a useful Banach space of
functions with applications in time-frequency analysis, the theory of pseudo-differential …

Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those
parts of mathematics and its applications that use the struc ture of translations and …

The modulation spaces Ms p, q (Rm), s∈ R, 1≤ p, q≤∞ to be discussed in this paper are
Banach spaces of tempered distributions σ on Rm, which are characterized by the behaviour …

This note provides historical perspective and background on the motivations which led to the
invention of the modulation spaces by the author almost 25 years ago, as well as comments …

Abstract The Density Theorem for Gabor Frames is one of the fundamental results of time-
frequency analysis. This expository survey attempts to reconstruct the long and very involved …

We describe various basic facts about Gabor multipliers and their continuous analogue
which we will call STFT-multipliers. These operators are obtained by going from the signal …

Convolutional Neural Networks have established a new standard in many machine learning
applications not only in image but also in audio processing. In this contribution we …

Using Gabor analysis, we give a complete characterization of all lattice sampling and
interpolating sequences in the Fock space of polyanalytic functions, displaying a “Nyquist …

A Gabor or Weyl-Heisenberg frame for $ L^ 2 (\mathbb {R}^ d) $ is generated by time-
frequency shifts of a square-integrable function, the Gabor atom, along a time-frequency …

Quantum harmonic analysis on phase space is shown to be linked with localization
operators. The convolution between operators and the convolution between a function and …