36 citations · 36 across the 1 of their papers we have counts for
6 papers
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…
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…
Harmonic analysis with respect to heat kernel measure
Brian C. Hall
I review certain results in harmonic analysis for systems whose configuration space is a compact Lie group. The results described involve a heat kernel measure, which plays the sam…
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…
Holomorphic Methods in Mathematical Physics
Brian C. Hall
This set of lecture notes gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commut…
Coherent states, Yang-Mills theory, and reduction
Brian C. Hall
This paper explains some of the ideas behind a prior joint work of the author with Bruce Driver on the canonical quantization of Yang-Mills theory on a spacetime cylinder. The idea…