Hardy spaces for non-compactly causal symmetric spaces and the most continuous spectrum

DOI10.1007/s00208-003-0409-xzbMath1037.43014arXivmath/0111172OpenAlexW2008006386MaRDI QIDQ1411993

Bernhard Krötz, Simon G. Gindikin, Gestur Olafsson

Publication date: 4 November 2003

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

Full work available at URL: https://arxiv.org/abs/math/0111172

zbMATH Keywords

Plancherel formulasemisimple symmetric spacescomplex crownmost continuous part of the spectrumnon-compactly causal spaces

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Semisimple Lie groups and their representations (22E46) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Boundary behavior of holomorphic functions of several complex variables (32A40) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Related Items (3)

Holomorphic \(H\)-spherical distribution vectors in principal series representations ⋮ Reflection positivity on spheres ⋮ Projections Separating Spectra for $\boldsymbol{L^2}$ on Pseudounitary Groups $\boldsymbol{{\mathrm U}(p,q)}$

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Causal compactification and Hardy spaces for spaces of Hermitian type.
• The holomorphic discrete series for affine symmetric spaces. I
• Plancherel formula for reductive symmetric spaces
• Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series
• The \(c\)-function for non-compactly causal symmetric spaces
• Laplace and Segal--Bargmann transforms on Hermitian symmetric spaces and orthogonal poly\-nomials.
• Stein extensions of Riemannian symmetric spaces and dualities of orbits on flag manifolds
• Holomorphy and convexity in Lie theory
• On Stein extensions of real symmetric spaces
• Holomorphic extensions of representations. I: Automorphic functions
• The Plancherel theorem for biinvariant Hilbert spaces
• The Plancherel decomposition for a reductive symmetric space. I: Spherical functions
• The Plancherel decomposition for a reductive symmetric space. II: Representation theory
• Holomorphic extensions of representations. II: Geometry and harmonic analysis
• Berezin transform on real bounded symmetric domains
• Spherical unitary highest weight representations
• Analytic Extension of the Holomorphic Discrete Series
• The Analytic Continuation of the Discrete Series.I
• Causal compactification and Hardy spaces
• Spherical representations and mixed symmetric spaces
• Causal compactification of compactly causal spaces
• Matrix analogues of the beta function and Plancherel's formula for Berezin kernel representations
• Complex crowns of Riemannian symmetric spaces and non-compactly causal symmetric spaces
• Meixner functions and polynomials related to Lie algebra representations

This page was built for publication: Hardy spaces for non-compactly causal symmetric spaces and the most continuous spectrum