Boundary values of holomorphic functions, singular unitary representations of \(O(p,q)\), and their limits as \(q\to\infty\)

DOI10.1007/BF02355796zbMath0909.22025OpenAlexW2022671461MaRDI QIDQ1375167

Grigori Olshanski, Yuriĭ A. Neretin

Publication date: 14 February 1999

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02355796

zbMATH Keywords

manifoldSobolev spacesLie groupHilbert spacesStiefel manifoldrepresentation theoryhighest weight representationboundary operatorsholomorphic functionsboundary valuesnoncommutative harmonic analysissingular representationsspherical complementary series representation

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Semisimple Lie groups and their representations (22E46) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items (max. 100)

Plancherel formula for Berezin deformation of \(L^{2}\) on Riemannian symmetric space ⋮ Groups of hierarchomorphisms of trees and related Hilbert spaces ⋮ Degenerate principal series representations and their holomorphic extensions ⋮ Tensor products of complementary series of rank one Lie groups ⋮ Degenerate principal series representations of \(\mathrm{SO}(p+1,p)\) ⋮ Grigori Iosifovich Olshanski ⋮ Hua-type integrals over unitary groups and over projective limits of unitary groups

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