Bounds on the Segal-Bargmann transform of L^p functions
Mathematical Physics
2007-05-23 v1 math.MP
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.
Keywords
Cite
@article{arxiv.math-ph/0103001,
title = {Bounds on the Segal-Bargmann transform of L^p functions},
author = {Brian C. Hall},
journal= {arXiv preprint arXiv:math-ph/0103001},
year = {2007}
}
Comments
To appear in J. Fourier Analysis and Applications