Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591991 | Journal of Functional Analysis | 2008 | 26 Pages |
Abstract
We consider the Segal–Bargmann transform on 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 dual 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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