Boundary Measures for Symmetric Domains and Integral Formulas for the Discrete Wallach Points

Jonathan Arazy; Harald Upmeier

doi:10.1007/s00020-003-1168-5

Boundary Measures for Symmetric Domains and Integral Formulas for the Discrete Wallach Points

Jonathan Arazy, Harald Upmeier

Department of Mathematics

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

Abstract

Let B be an irreducible hermitian symmetric domain of rank r in ℂ ^d and let G := Aut(B) the group of all biholomorphic automorphisms of B. We construct explicit integral formulas for the G-invariant inner products on spaces of holomorphic functions on B associated with the discrete Wallach points and the so-called embedded Wallach points, by means of integration on G-orbits on the boundary ∂ B of B and of invariant differential operators acting on symmetric domains of lower rank.

Original language	English
Pages (from-to)	375-434
Number of pages	60
Journal	Integral Equations and Operator Theory
Volume	47
Issue number	4
DOIs	https://doi.org/10.1007/s00020-003-1168-5
State	Published - 2003

Bibliographical note

Funding Information:
The authors gratefully acknowledge partial financial support by the Erwin-Schrö-dinger Institute (Vienna) and the German-Israeli-Foundation (GIF, grant No. I-415-023.06/95).

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-003-1168-5

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abstract = "Let B be an irreducible hermitian symmetric domain of rank r in ℂ d and let G := Aut(B) the group of all biholomorphic automorphisms of B. We construct explicit integral formulas for the G-invariant inner products on spaces of holomorphic functions on B associated with the discrete Wallach points and the so-called embedded Wallach points, by means of integration on G-orbits on the boundary ∂ B of B and of invariant differential operators acting on symmetric domains of lower rank.",

author = "Jonathan Arazy and Harald Upmeier",

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N2 - Let B be an irreducible hermitian symmetric domain of rank r in ℂ d and let G := Aut(B) the group of all biholomorphic automorphisms of B. We construct explicit integral formulas for the G-invariant inner products on spaces of holomorphic functions on B associated with the discrete Wallach points and the so-called embedded Wallach points, by means of integration on G-orbits on the boundary ∂ B of B and of invariant differential operators acting on symmetric domains of lower rank.

AB - Let B be an irreducible hermitian symmetric domain of rank r in ℂ d and let G := Aut(B) the group of all biholomorphic automorphisms of B. We construct explicit integral formulas for the G-invariant inner products on spaces of holomorphic functions on B associated with the discrete Wallach points and the so-called embedded Wallach points, by means of integration on G-orbits on the boundary ∂ B of B and of invariant differential operators acting on symmetric domains of lower rank.

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ER -

Boundary Measures for Symmetric Domains and Integral Formulas for the Discrete Wallach Points

Abstract

Bibliographical note

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