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Holomorphic retractions and boundary Berezin transforms
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SYSNO ASEP 0334144 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Holomorphic retractions and boundary Berezin transforms Title Holomorfní retrakce a hraniční Berezinovy transformace Author(s) Arazy, J. (IL)
Engliš, Miroslav (MU-W) RID, ORCID, SAI
Kaup, W. (DE)Source Title Annales de l'Institut Fourier - ISSN 0373-0956
Roč. 59, č. 2 (2009), s. 641-657Number of pages 17 s. Language eng - English Country FR - France Keywords Berezin transform ; Cartan domain ; convolution operator Subject RIV BA - General Mathematics R&D Projects IAA1019304 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000266138300009 Annotation In in 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 mu 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 settle measure mu(F) on F uniquely determined by mu. In this article, we give all explicit formula for mu(F) in terms of F, showing in particular that for measures mu corresponding to the Berezin transforms the measures mu(F) 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 oil these domains which arises as the boundary limit of geodesic symmetries. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2010
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