Localization operators and exponential weights for modulation spaces
type: Item
instance of: scholarly article
title: Localization operators and exponential weights for modulation spaces
zbMATH Open document ID: 1171.47303
author: Elena Cordero
author: Luigi Rodino
author: Nenad Teofanov
author: Stevan Pilipović
published in: Mediterranean Journal of Mathematics
publication date: 2006-09-28T00:00:00Z
full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary
review text: The authors extend the study of localization operators in [\textit{E.\,Cordero} and \textit{K.\,Gröchenig}, J.~Funct.\ Anal.\ 205, No.\,1, 107--131 (2003; Zbl 1047.47038)] by considering the case of their window functions belonging to the Gelfand--Shilov space \(S^{(1)}\) of analytic functions, and the symbols from its strong dual, the space of tempered ultra-distributions of Beurling type. Necessary and sufficient conditions for the localization operators to be bounded or to belong to a Schatten class are given. The results are formulated in terms of modulation spaces with weights which may have exponential growth. In particular, the authors study symbols defined by ultra-distributions with compact support, that give trace class localization operators.
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 44A05
zbMATH DE Number: 5058638
zbMATH Keywords: localisation operator
zbMATH Keywords: ultradistributions
zbMATH Keywords: Gelfand-Shilov type spaces
zbMATH Keywords: modulation space
zbMATH Keywords: Wigner distribution
zbMATH Keywords: short-time Fourier transform
zbMATH Keywords: Schatten class
MaRDI profile type: Publication
OpenAlex ID: W2089789277
DOI: 10.1007/S00009-005-0052-8
description: scientific article