Mapping properties for the Bargmann transform on modulation spaces
type: Item
instance of: scholarly article
title: Mapping properties for the Bargmann transform on modulation spaces
zbMATH Open document ID: 1260.42014
author: Mikael Signahl
author: Joachim Toft
published in: Journal of Pseudo-Differential Operators and Applications
publication date: 2012-11-09T00:00:00Z
review text: The authors investigate mapping properties for the Bargmann transform on an extended family of modulation spaces \(M(\omega, \mathcal{B})\) with weights \(\omega\) and translation invariant BF-spaces \(\mathcal{B}\). They prove that this transform is isometric and bijective from modulaton spaces \(M(\omega, \mathcal{B})\) to convenient Banach spaces \(A(\omega, \mathcal{B})\) of analytic functions. The authors use the results to establish mapping properties of Berezin-Toeplitz operators and get spectral properties of harmonic oscillators on modulation spaces.
reviewed by: Koichi Saka
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 44A20
Mathematics Subject Classification ID: 47B35
zbMATH DE Number: 6104308
zbMATH Keywords: Bargmann transform
zbMATH Keywords: modulation space
zbMATH Keywords: harmonic oscillator
zbMATH Keywords: short-time Fourier transform
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: weight
zbMATH Keywords: translation invariant BF-space
MaRDI profile type: Publication
full work available at URL: s11868-011-0039-0
OpenAlex ID: W1998639520
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DOI: 10.1007/S11868-011-0039-0
description: scientific article; zbMATH DE number 6104308