Generalized Bernstein-Reznikov integrals

DOI10.1007/s00208-010-0516-4zbMath1207.42021arXiv0906.2874OpenAlexW3097985557MaRDI QIDQ621302

Toshiyuki Kobayashi, Michael Pevzner, Jean-Louis Clerc, Bent Orsted

Publication date: 2 February 2011

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.2874

zbMATH Keywords

Fourier transformharmonic polynomialsHankel transformsymplectic formBernstein-Reznikov integralBochner identitytriple integral

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Generalized hypergeometric series, ({}_pF_q) (33C20) Spherical harmonics (33C55)

Related Items (22)

Knapp-Stein type intertwining operators for symmetric pairs ⋮ F-method for symmetry breaking operators ⋮ Singular conformally invariant trilinear forms. I: The multiplicity one theorem ⋮ Real double flag varieties for the symplectic group ⋮ Singular conformally invariant trilinear forms. II: The higher multiplicity case ⋮ Symmetry breaking for representations of rank one orthogonal groups ⋮ Symmetry breaking operators for strongly spherical reductive pairs ⋮ Conformally invariant trilinear forms on the sphere ⋮ On the degenerate principal series of complex symplectic groups ⋮ Geometric analysis on small unitary representations of \(\text{GL}(N, \mathbb R)\) ⋮ Singular invariant trilinear forms and covariant (bi-)differential operators under the conformal group ⋮ Bounded multiplicity theorems for induction and restriction ⋮ Finite multiplicity theorems for induction and restriction ⋮ Symmetric pairs with finite-multiplicity property for branching laws of admissible representations ⋮ Classification of finite-multiplicity symmetric pairs ⋮ Invariant trilinear forms on spherical principal series of real rank one semisimple Lie groups ⋮ Double Gegenbauer expansion of |s–t|^α ⋮ Tensor products of complementary series of rank one Lie groups ⋮ A program for branching problems in the representation theory of real reductive groups ⋮ Extensions of the classical theorems for very well-poised hypergeometric functions ⋮ Summation formulas for GJMS-operators and \(Q\)-curvatures on the Möbius sphere ⋮ Multiplicity in restricting small representations

Cites Work

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• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
• Odd symplectic groups
• Intertwining operators for semisimple groups. II
• Discrete decomposability of the restriction of \(A_q(\lambda)\) with respect to reductive subgroups. II: Micro-local analysis and asymptotic \(K\)-support
• Analytic continuation of representations and estimates of automorphic forms
• Automorphic pseudodifferential analysis and higher level Weyl calculi
• Integral formula of the unitary inversion operator for the minimal representation of \(\text{O}(p,q)\)
• Composition formulas in the Weyl calculus
• Invariant triple products

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