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Annales de l’institut Fourier
Article . 2009 . Peer-reviewed
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Article . 2009
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Holomorphic retractions and boundary Berezin transforms

Authors: Arazy, J.; Engliš, M. (Miroslav); Kaup, W.;

Holomorphic retractions and boundary Berezin transforms

Abstract

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 μ 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 μ F on F uniquely determined by μ . In this article, we give an explicit formula for μ F in terms of F , showing in particular that for measures μ corresponding to the Berezin transforms the measures μ 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 on these domains which arises as the boundary limit of geodesic symmetries.

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Czech Republic
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Keywords

Berezin transform, Idempotents, Peirce decompositions, convolution operator, Banach algebras of differentiable or analytic functions, \(H^p\)-spaces, Linear operators on function spaces (general), Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), Cartan domain, Differential geometry of symmetric spaces

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
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