Bounds on the Segal-bargmann Transform of L Functions
نویسنده
چکیده
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(R, ρ), where ρ is 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. I also give a single necessary-and-sufficient condition for a holomorphic function to be the transform of a function f such that any derivative of f multiplied by any polynomial is in L(R, ρ). Finally I give some weaker but dimensionindependent conditions.
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