Fock spaces connected with spherical mean operator and associated operators
type: Item
instance of: scholarly article
title: Fock spaces connected with spherical mean operator and associated operators
zbMATH Open document ID: 1193.47029
author: C. Baccar
author: Slim Omri
author: L. T. Rachdi
published in: Mediterranean Journal of Mathematics
publication date: 2009-07-14T00:00:00Z
review text: Following ideas of \textit{V.\,Bargmann} [Commun.\ Pure Appl.\ Math.\ 14, 187--214 (1961; Zbl 0107.09102); Proc.\ Natl.\ Acad.\ Sci.\ USA 48, 199--204 (1962; Zbl 0107.09103)] and \textit{F.\,M.\thinspace Cholewinsky} [SIAM J.~Math.\ Anal.\ 15, 177--202 (1984; Zbl 0596.46017)], the authors define the Fock space \(F\) associated with the spherical mean operator to be the space of entire functions on \(\mathbb C\times\mathbb C^n\), which are even in the first variable and square integrable with respect to a certain measure expressed through the Mac Donald function \(K_{(n-1)/2}(\cdot)\). Some results for the Segal-Bargmann transform and for Toeplitz operators in this space are established.
reviewed by: Boris Rubin
Mathematics Subject Classification ID: 47B32
Mathematics Subject Classification ID: 44A99
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 46E22
zbMATH DE Number: 5578113
zbMATH Keywords: Fock spaces
zbMATH Keywords: the spherical mean operator
zbMATH Keywords: Segal-Bargmann transform
zbMATH Keywords: Toeplitz operators
MaRDI profile type: Publication
full work available at URL: s00009-009-0164-7
OpenAlex ID: W2068067281
DOI: 10.1007/S00009-009-0164-7
description: scientific article; zbMATH DE number 5578113