The Segal-Bargmann transform for noncompact symmetric spaces of the complex type
Quantum Physics
2007-10-01 v2 Mathematical Physics
Differential Geometry
math.MP
Abstract
We consider the generalized Segal-Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal-Bargmann transform is a unitary map onto a certain L^2 space of meromorphic functions. For general functions, we give an inversion formula for the Segal-Bargmann transform, involving integration against an "unwrapped" version of the heat kernel for the dual compact symmetric space. Both results involve delicate cancellations of singularities.
Keywords
Cite
@article{arxiv.quant-ph/0409118,
title = {The Segal-Bargmann transform for noncompact symmetric spaces of the complex type},
author = {Brian C. Hall and Jeffrey J. Mitchell},
journal= {arXiv preprint arXiv:quant-ph/0409118},
year = {2007}
}
Comments
28 pages. Minor corrections made. To appear in J. Functional Analysis