Analytic factorization of Lie group representations

DOI10.1016/j.jfa.2011.10.002zbMath1234.22006arXiv0910.0177OpenAlexW2964028364MaRDI QIDQ656214

Bernhard Krötz, Christoph Lienau, Heiko Gimperlein

Publication date: 17 January 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.0177

zbMATH Keywords

convolutionrepresentationLie groupfactorizationFréchet spacetest functionanalytic vectorDixmier-Malliavinmoderate growth, superexponential decay

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Rings and algebras of continuous, differentiable or analytic functions (46E25)

Related Items (6)

Continuity of LF-algebra representations associated to representations of Lie groups ⋮ On the structure of analytic vectors for the Schrödinger representation ⋮ Analytic Dirac approximation for real linear algebraic groups ⋮ Factorization in Denjoy-Carleman classes associated to representations of \((\mathbb{R}^d, +)\) ⋮ On Sobolev norms for Lie group representations ⋮ Smooth Fréchet globalizations of Harish-Chandra modules

Cites Work

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• Analytic vectors
• Analytic representation theory of \((\mathbb R,+)\)
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Irreducibility of certain entire functions with applications to harmonic analysis
• Smooth Fréchet globalizations of Harish-Chandra modules
• Analytic domination by fractional powers of a positive operator
• Analytic representation theory of Lie groups: general theory and analytic globalizations of Harish-Chandra modules
• Note on Continuous Representations of Lie Groups

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