Bounds on the Segal-Bargmann transform of Lp functions
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 Lp(Rd) 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.
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