The Segal-Bargmann transform for noncompact symmetric spaces of the complex type

Details The Segal-Bargmann transform for noncompact symmetric spaces of the complex type The Segal-Bargmann transform for noncompact symmetric spaces of the complex type

2004-09-17

arxiv.org/abs/quant-ph/0409118v2

J. Functional Analysis 227 (2005), 338-371

Physics

Quantum Physics

28 pages. Minor corrections made. To appear in J. Functional Analysis

Scientific paper

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.

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