Gabor Analysis in Weighted Amalgam Spaces

Gabor Analysis in Weighted Amalgam Spaces

Gabor frames {e2πinβ·xg(x− kα)}n,k∈Zd provide series representations not only of functions in L(R) but of the entire range of spaces M ν known as the modulation spaces. Membership of a function or distribution f in the modulation space is characterized by a sequence-space norm of the Gabor coefficients of f depending only on the magnitudes of those coefficients, and the Gabor series representat...

Multi-window Gabor Frames in Amalgam Spaces

We show that multi-window Gabor frames with windows in the Wiener algebra W (L∞, `) are Banach frames for all Wiener amalgam spaces. As a by-product of our results we prove the canonical dual of a Gabor frame with a continuous generator in the Wiener algebra also belongs to this space. Our proofs are mostly based on recent noncommutative versions of Wiener’s 1/f lemma.

Wiener Amalgam Spaces for the Fundamental Identity of Gabor Analysis

In the last decade it has become clear that one of the central themes within Gabor analysis (with respect to general timefrequency lattices) is a duality theory for Gabor frames, including the Wexler-Raz biorthogonality condition, the Ron-Shen’s duality principle or Janssen’s representation of a Gabor frame operator. All these results are closely connected with the so-called Fundamental Identit...

Amalgam Spaces and Generalized Harmonic Analysis

It is the purpose of this short note to indicate in which way certain amalgam spaces, deened in the spirit of N. Wiener, can be used to deal with questions arising in generalized harmonic analysis in several dimensions. In some sense these results are natural extensions of corresponding one-dimensional results due to N. Wiener (e.g. Theorem 29 in his book 33i]). Amalgams are taken with respect ...

Spline-type Spaces in Gabor Analysis