Realization of the invariant inner products on the highest quotients of the composition series

DOI10.1007/BF02384859zbMath0767.46015MaRDI QIDQ1197453

Jonathan Arazy

Publication date: 16 January 1993

Published in: Arkiv för Matematik (Search for Journal in Brave)

zbMATH Keywords

Besov spacesDirichlet spacebiholomorphic automorphismsWallach setHilbert spaces of analytic functionsbounded symmetric domain of tube typeFaraut-Koranyi formulaeinvariant inner productsinvariant under the unitary actionirreducible \(JB^*\)-algebra of finite dimension and rankPeter-Weyl orthogonal expansion

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Hilbert spaces of continuous, differentiable or analytic functions (46E20)

Related Items (4)

Hankel forms of arbitrary weight over a symmetric domain via the transvectant ⋮ Invariant spaces of holomorphic functions on the Siegel upper half-space ⋮ Actions of the Möbius group on analytic functions ⋮ Composition series for analytic continuations of holomorphic discrete series representations of \(\text{SU}_{p,q}\)

Cites Work

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• Möbius invariant spaces on the unit ball
• Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen Räumen
• Function spaces and reproducing kernels on bounded symmetric domains
• Jordan Algebras and Harmonic Analysis on Symmetric Spaces
• Function Theory on Cartan Domains and the Berezin-Toeplitz Symbol Calculus
• Hankel Operators on Weighted Bergman Spaces
• Composition Series for Analytic Continuations of Holomorphic Discrete Series Representations of SU(n, n)
• Mobius Invariant Hilbert Spaces of Holomorphic Functions in the Unit Ball of ℂ n
• Membership of Hankel Operators on the Ball in Unitary Ideals
• QUANTIZATION IN COMPLEX SYMMETRIC SPACES

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