Heat kernel transform for nilmanifolds associated to the Heisenberg group

DOI10.4171/RMI/535zbMath1153.22009arXivmath/0607134OpenAlexW2002934238MaRDI QIDQ935487

Yuan Xu, Bernhard Krötz, Sundaram Thangavelu

Publication date: 6 August 2008

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607134

zbMATH Keywords

Heisenberg groupBergman spacesheat kernelnilmanifoldsHermite and Laguerre functions

Mathematics Subject Classification ID

Heat equation (35K05) Analysis on real and complex Lie groups (22E30) Analysis on other specific Lie groups (43A80) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Subelliptic equations (35H20)

Related Items (3)

An analogue of Ingham's theorem on the Heisenberg group ⋮ The Poisson transform on a compact real analytic Riemannian manifold ⋮ Heat kernel transform on nilmanifolds associated to H-type groups

Cites Work

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• The theta transform and the Heisenberg group
• The Segal-Bargmann transform on a symmetric space of compact type
• The Segal-Bargmann ``coherent state transform for compact Lie groups
• Harmonic analysis on the Heisenberg group
• Compact Heisenberg manifolds as CR manifolds
• Translation-invariant subspaces in L\(^2\) of a compact nilmanifold. I
• The heat kernel transform for the Heisenberg group
• On a Hilbert space of analytic functions and an associated integral transform part I
• Inversions of Hermite Semigroup
• Harmonic Analysis on Nilmanifolds

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