Gabor frames and time-frequency analysis of distributions
type: Item
instance of: scholarly article
title: Gabor frames and time-frequency analysis of distributions
zbMATH Open document ID: 0887.46017
author: H. G. Feichtinger
author: Karlheinz Gröchenig
published in: Journal of Functional Analysis
publication date: 1998-05-25T00:00:00Z
review text: The authors show that the correct class of spaces which can be characterized by the magnitude of the coefficients \(C_{k,n}\) in the Gabor expansion \(\sum_{k,n} C_{k,n}e^{2\pi in\alpha x}g(x- k\beta)\) is the class of modulation spaces. They prove that the Gabor frame operator is invertible on the modulation space if and only if it is invertible on \(L^2\) and the atom \(g\) is in a suitable space of test functions. They show that an analogous statement for wavelet theory is false.
Mathematics Subject Classification ID: 46F10
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1077106
zbMATH Keywords: Gabor expansion
zbMATH Keywords: modulation spaces
zbMATH Keywords: Gabor frame operator
zbMATH Keywords: wavelet theory
reviewed by: Ludvík Janoš
MaRDI profile type: Publication
full work available at URL: jfan.1996.3078
OpenAlex ID: W2041334070
DOI: 10.1006/JFAN.1996.3078
description: scientific article; zbMATH DE number 1077106