Holomorphic retractions and boundary berezin transforms

Jonathan Arazy, Miroslav Engliš, Wilhelm Kaup

Research output: Contribution to journalArticlepeer-review


In an earlier paper, the first two authors have shown that the convolution of a function f continuous on the closure of a Cartan domain and a K- invariant finite measure a. on that domain is again continuous on the closure, and, moreover, its restriction to any boundary face F depends only on the restriction of f to F and is equal to the convolution, in F, of the latter restriction with some measure (if on F uniquely determined by μ In this article, we give an explicit formula for μF in terms of F, showing in particular that for measures μ corresponding to the Berezin transforms the measures p again correspond to Berezin transforms, but with a shift in the value of the Wallach parameter. Finally, we also obtain a nice and simple description of the holomorphic retraction on these domains which arises as the boundary limit of geodesic symmetries.

Original languageEnglish
Pages (from-to)641-657
Number of pages17
JournalAnnales de l'Institut Fourier
Issue number2
StatePublished - 2009


  • Berezin transform
  • Cartan domain
  • Convolution operator

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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