01-84 Brian C. Hall

Bounds on the Segal-Bargmann transform of L^p functions (65K, Latex) Mar 1, 01

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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.

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