Berezin transform for solvable groups

Jonathan Arazy; Harald Upmeier

doi:10.1023/B:ACAP.0000024192.68563.8d

Berezin transform for solvable groups

Jonathan Arazy, Harald Upmeier

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the Berezin transform in the context of solvable groups AN (acting on homogeneous cones and Siegel domains) and determine its spectral decomposition, using an explicit integral kernel representation for the associated 'eigen-operators' in terms of multivariable hypergeometric functions.

Original language	English
Pages (from-to)	5-28
Number of pages	24
Journal	Acta Applicandae Mathematicae
Volume	81
Issue number	1
DOIs	https://doi.org/10.1023/B:ACAP.0000024192.68563.8d
State	Published - Mar 2004

Bibliographical note

Funding Information:
★Research partially supported by the German–Israel Foundation 17.6/2001.

Keywords

Berezin transform
Correspondence principle
Euclidean Jordan algebras
Homogeneous Siegel domains
Hypergeometric functions
Reproducing kernels
Solvable groups
Summability kernels
Symmetric cones

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1023/B:ACAP.0000024192.68563.8d

Cite this

@article{a0275a59410d435390b24ca5978e7b89,

title = "Berezin transform for solvable groups",

abstract = "We study the Berezin transform in the context of solvable groups AN (acting on homogeneous cones and Siegel domains) and determine its spectral decomposition, using an explicit integral kernel representation for the associated 'eigen-operators' in terms of multivariable hypergeometric functions.",

keywords = "Berezin transform, Correspondence principle, Euclidean Jordan algebras, Homogeneous Siegel domains, Hypergeometric functions, Reproducing kernels, Solvable groups, Summability kernels, Symmetric cones",

author = "Jonathan Arazy and Harald Upmeier",

note = "Funding Information: ★Research partially supported by the German–Israel Foundation 17.6/2001.",

year = "2004",

month = mar,

doi = "10.1023/B:ACAP.0000024192.68563.8d",

language = "English",

volume = "81",

pages = "5--28",

journal = "Acta Applicandae Mathematicae",

issn = "0167-8019",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Berezin transform for solvable groups

AU - Arazy, Jonathan

AU - Upmeier, Harald

N1 - Funding Information: ★Research partially supported by the German–Israel Foundation 17.6/2001.

PY - 2004/3

Y1 - 2004/3

N2 - We study the Berezin transform in the context of solvable groups AN (acting on homogeneous cones and Siegel domains) and determine its spectral decomposition, using an explicit integral kernel representation for the associated 'eigen-operators' in terms of multivariable hypergeometric functions.

AB - We study the Berezin transform in the context of solvable groups AN (acting on homogeneous cones and Siegel domains) and determine its spectral decomposition, using an explicit integral kernel representation for the associated 'eigen-operators' in terms of multivariable hypergeometric functions.

KW - Berezin transform

KW - Correspondence principle

KW - Euclidean Jordan algebras

KW - Homogeneous Siegel domains

KW - Hypergeometric functions

KW - Reproducing kernels

KW - Solvable groups

KW - Summability kernels

KW - Symmetric cones

UR - http://www.scopus.com/inward/record.url?scp=3543113827&partnerID=8YFLogxK

U2 - 10.1023/B:ACAP.0000024192.68563.8d

DO - 10.1023/B:ACAP.0000024192.68563.8d

M3 - Article

AN - SCOPUS:3543113827

SN - 0167-8019

VL - 81

SP - 5

EP - 28

JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

IS - 1

ER -

Berezin transform for solvable groups

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this