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Holomorphic Sobolev spaces and the generalized Segal-Bargmann transform | | Brian C. Hall
; Wicharn Lewkeeratiyutkul
; | | Date: |
16 Jun 2004 | | Journal: | J. Functional Analysis 217 (2004) 192--220 DOI: 10.1016/j.jfa.2004.03.018 | | Subject: | Mathematical Physics MSC-class: 81S30; 22E30 | math-ph math.MP | | 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. | | Source: | arXiv, math-ph/0406033 | | Services: | Forum | Review | PDF | Favorites | |
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