Holomorphic Sobolev spaces and the generalized Segal-Bargmann transform

Details Holomorphic Sobolev spaces and the generalized Segal-Bargmann transform Holomorphic Sobolev spaces and the generalized Segal-Bargmann transform

2004-06-16

arxiv.org/abs/math-ph/0406033v1

J. Functional Analysis 217 (2004) 192--220

Physics

Mathematical Physics

To appear in J. Functional Analysis

Scientific paper

10.1016/j.jfa.2004.03.018

We 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.

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