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arXiv · 0707.0874

Isometry theorem for the Segal-Bargmann transform on noncompact symmetric spaces of the complex type

Brian C. Hall·Jeffrey J. Mitchell
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Abstract

We consider the Segal-Bargmann transform for a noncompact symmetric space of the complex type. We establish isometry and surjectivity theorems for the transform, in a form as parallel as possible to the results in the compact case. The isometry theorem involves integration over a tube of radius R in the complexification, followed by analytic continuation with respect to R. A cancellation of singularities allows the relevant integral to have a nonsingular extension to large R, even though the function being integrated has singularities.

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Brian C. Hall, Jeffrey J. Mitchell. 2007-08-01. Isometry theorem for the Segal-Bargmann transform on noncompact symmetric spaces of the complex type. https://doi.org/10.1016/j.jfa.2007.08.004

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