Holomorphic extension of eigenfunctions

DOI10.1007/S00208-009-0379-8zbMath1181.58022arXiv0812.0724OpenAlexW2148264260MaRDI QIDQ734962

Bernhard Krötz, Henrik Schlichtkrull

Publication date: 14 October 2009

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

Full work available at URL: https://arxiv.org/abs/0812.0724

zbMATH Keywords

holomorphic extensionpartial differential equationsCasimir operatorRiemannian symmetric spaceeigenfunctions of the Laplace-Beltrami operatorthe complex crown

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) General properties and structure of complex Lie groups (22E10) Ordinary differential equations on complex manifolds (34M45) Miscellaneous topics in partial differential equations (35R99) Connections of harmonic functions with differential equations in higher dimensions (31B35) Holomorphic functions of several complex variables (32A10)

Related Items (2)

On weighted Bergman spaces of a domain with Levi-flat boundary II. ⋮ The complex crown for homogeneous harmonic spaces

Cites Work

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• Eigenfunctions of invariant differential operators on a symmetric space
• The geometry of Grauert tubes and complexification of symmetric spaces
• On Stein extensions of real symmetric spaces
• On certain domains in cycle spaces of flag manifolds
• Holomorphic extensions of representations. I: Automorphic functions
• Holomorphic extensions of representations. II: Geometry and harmonic analysis

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