On the images of Sobolev spaces under the heat kernel transform on the Heisenberg group

DOI10.1002/MANA.201100233zbMath1277.42027OpenAlexW2019637360MaRDI QIDQ2852506

Ramakrishnan Radha, Venku Naidu Dogga, Sundaram Thangavelu

Publication date: 9 October 2013

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

Full work available at URL: https://doi.org/10.1002/mana.201100233

zbMATH Keywords

Sobolev spaceBergman spaceHeisenberg groupunitary representationsublaplacianSchwartz classheat kernel transform

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Analysis on real and complex Lie groups (22E30) Analysis on other specific Lie groups (43A80)

Related Items (2)

On the images of Dunkl-Sobolev spaces under the Schrödinger semigroup associated to Dunkl operators ⋮ On the images of Sobolev spaces under the Schrödinger semigroup

Cites Work

• Unnamed Item
• Holomorphic Sobolev spaces and the generalized Segal-Bargmann transform
• Gutzmer's formula and Poisson integrals on the Heisenberg group
• Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform
• The Segal-Bargmann transform on a symmetric space of compact type
• The Segal-Bargmann ``coherent state transform for compact Lie groups
• An introduction to the uncertainty principle. Hardy's theorem on Lie groups. With a foreword by Gerald B. Folland
• Holomorphic Sobolev spaces associated to compact symmetric spaces
• The heat kernel transform for the Heisenberg group
• Harmonic Analysis in Phase Space. (AM-122)
• An analogue of Gutzmer's formula for Hermite expansions

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