Holomorphic Sobolev spaces and the generalized Segal-Bargmann transform

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dc.creatorHall, Brian C.
dc.creatorLewkeeratiyutkul, Wicharn
dc.date2004-06-16
dc.date.accessioned2026-07-07T04:31:15Z
dc.date.available2026-07-07T04:31:15Z
dc.descriptionWe consider the generalized Segal-Bargmann transform C_t for a compact group K, introduced in B. C. Hall, J. Funct. Anal. 122 (1994), 103-151. Let K_C denote the complexification of K. We give a necessary-and-sufficient pointwise growth condition for a holomorphic function on K_C to be the image under C_t of a C-infinity function on K. We also characterize the image under C_t of Sobolev spaces on K. The proofs make use of a holomorphic version of the Sobolev embedding theorem.
dc.descriptionTo appear in J. Functional Analysis
dc.identifierhttps://arxiv.org/abs/math-ph/0406033
dc.identifierhttp://arxiv.org/abs/math-ph/0406033
dc.identifierJ. Functional Analysis 217 (2004) 192--220
dc.identifierdoi:10.1016/j.jfa.2004.03.018
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57749
dc.subjectMathematical Physics
dc.subject81S30; 22E30
dc.titleHolomorphic Sobolev spaces and the generalized Segal-Bargmann transform
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