Berezin transform for solvable groups

Jonathan Arazy, Harald Upmeier

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)5-28
Number of pages24
JournalActa Applicandae Mathematicae
Issue number1
StatePublished - Mar 2004

Bibliographical note

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


  • 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


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