Brian C. Hall
Bounds on the Segal-Bargmann transform of L^p functions
(65K, Latex)
ABSTRACT. 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 over R^d with respect to a Gaussian
measure. The proof relies on a family of inversion formulas for the
Segal-Bargmann transform, which can be "tuned" to give the best
estimates for a given value of p.