Bounds on the Segal-Bargmann transform of L^p functions

2001/03/01 by Brian C. Hall
Physics and Astronomy · Mathematics · #math-ph #math.MP

paper · pdf

published as J. Fourier Analysis and Applications, Vol. 7 (2001), 553-569 · To appear in J. Fourier Analysis and Applications

arxiv created 2001/03/01 · arxiv updated 2009/11/30

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(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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