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Holomorphic Sobolev spaces and the generalized Segal-Bargmann transform

Brian C. Hall·Wicharn Lewkeeratiyutkul
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Abstract

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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Brian C. Hall, Wicharn Lewkeeratiyutkul. 2004-06-16. Holomorphic Sobolev spaces and the generalized Segal-Bargmann transform. https://doi.org/10.1016/j.jfa.2004.03.018

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