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math-ph2004★ 36 cited
Holomorphic Sobolev spaces and the generalized Segal-Bargmann transform
Brian C. Hall, Wicharn Lewkeeratiyutkul
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 o…
math-ph2001
Bounds on the Segal-Bargmann transform of L^p functions
Brian C. Hall
This paper gives necessary conditions and slightly stronger sufficient conditions for a holomorphic function to be the Segal-Bargmann transform of a function in L^p(R^d) with respe…
math-ph2000
An Elementary Introduction to Groups and Representations
Brian C. Hall
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they h…