Two integral operators in Clifford analysis
type: Item
instance of: scholarly article
title: Two integral operators in Clifford analysis
zbMATH Open document ID: 1182.30082
author: J. Martínez
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-05-19T00:00:00Z
review text: Monogenic functions are generalizations of holomorphic functions in one complex variable to \(\mathbb{R}^{n+1}\) variable. Let \(M_2(\mathbb{R}^{n+1})\) be the monogenic Fock space obtained by the completion of the space of monogenic polynomials and \(\mathcal{F}_2(\mathbb{C}^n)\) be the Fock space of holomorphic functions in \(\mathbb{C}^n\) (Segal-Bargmann space). The objective of this paper is to study the connections between \(\mathcal{F}_2(\mathbb{C}^n)\) and \(M_2(\mathbb{R}^{n+1})\). Two integral operators are defined connecting these two spaces with the help of exponential functions in Clifford analysis.
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 46E20
zbMATH DE Number: 5555200
zbMATH Keywords: Segal-Bargmann space
zbMATH Keywords: monogenic Fock space
zbMATH Keywords: Clifford analysis
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.12.021
OpenAlex ID: W2068143599
cites work: Q3310867
cites work: Q4237149
cites work: Q4003806
cites work: Harmonic Analysis in Phase Space. (AM-122)
cites work: Q3995205
cites work: Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces
cites work: Q4878730
cites work: Q3729280
cites work: Q3794482
DOI: 10.1016/J.JMAA.2008.12.021
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description: scientific article; zbMATH DE number 5555200