Finite rank Hankel operators over the complex Wiener space
type: Item
instance of: scholarly article
title: Finite rank Hankel operators over the complex Wiener space
zbMATH Open document ID: 1072.47024
author: Thomas Deck
published in: Potential Analysis
publication date: 2005-05-13T00:00:00Z
review text: This paper discusses finite-rank small Hankel operators \(H_{b}\) on a Hilbert space of holomorphic, square integrable Wiener functionals, where \(b\) is called a finite-rank symbol, \(H_{b}\) is continuous and has finite rank. The tool used is the unitary equivalent representation of \(H_{b}\) on the Hilbert space of skeletons. The finite rank property is characterized in terms of a functional equation for the symbol \(b\), which generalizes the well-known equation \(b(z+w)=b(z)b(w)\). Also, polynomial finite-rank symbols are investigated in this paper.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 46E20
zbMATH DE Number: 2168220
zbMATH Keywords: small Hankel operators
zbMATH Keywords: holomorphic Wiener functions
zbMATH Keywords: chaos expansions
zbMATH Keywords: finite rank property
reviewed by: Ze-Hua Zhou
MaRDI profile type: Publication
full work available at URL: s11118-003-6458-7
OpenAlex ID: W4214921897
cites work: Hankel operators over the complex Wiener space
cites work: Hankel operators over complex manifolds.
cites work: A review of white noise analysis from a probabilistic standpoint
cites work: Q5687097
cites work: Q3244654
cites work: Q4252795
cites work: Bergman kernel asymptotics for generalized Fock spaces
cites work: Q5815839
cites work: Gaussian Hilbert Spaces
cites work: Weak Factorization in Periodic Fock Space
cites work: Hankel forms and the Fock space
cites work: A new look on Hankel forms over Fock space
cites work: Q3711155
cites work: Hankel forms on Fock space modulo \(C_ N\)
cites work: On the \(S_ 4\)-norm of a Hankel form
cites work: Q3349698
cites work: Hankel and Toeplitz operators on the Fock space
cites work: Properties of holomorphic Wiener functions -- skeleton, contraction, and local Taylor expansion
cites work: Q4207432
DOI: 10.1007/S11118-003-6458-7
description: scientific article; zbMATH DE number 2168220