Analogs of classical results on accumulated spectrograms, the sum of spectrograms of
eigenfunctions of localization operators, are established for Gabor multipliers. We show that …

Abstract For the Weyl-Heisenberg group, convolutions between functions and operators
were defined by Werner as a part of a framework called quantum harmonic analysis. We …

Matrices of operators with respect to frames are sometimes more natural and easier to
compute than the ones related to bases. The present work investigates such operators on …

The central topic in Gabor analysis is the set of Weyl-Heisenberg families, obtained from a
“window” g, by means of time-frequency shifts along some lattice Λ◃ ℝ2d. As a starting point …

This is a survey presenting an overview of the results describing the behavior of the
eigenvalues of compact Gabor–Toeplitz operators and Gabor multipliers. We introduce …

We consider Gabor localization operators $ G_ {\phi,\Omega} $ defined by two parameters,
the generating function $\phi $ of a tight Gabor frame $\{\phi_\lambda\} …

We consider Gabor systems generated by a window given by the hyperbolic secant function.
We show that such a system forms a Parseval frame for L 2 (ℝ) when the translations and …

The Fourier transforms of Laguerre functions play the same canonical role in wavelet
analysis as do the Hermite functions in Gabor analysis. We will use them as analyzing …

In this paper we investigate irregular Gabor frames. It is shown that for any Schwartz function
the family of its time–frequency shifts constitutes a weighted Gabor frame if only the lattice of …

In the early days of Gabor analysis it was a common to say that Gabor expansions of signals
are interesting due to the natural interpretation of Gabor coefficients, but unfortunately the …