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The Segal-Bargmann transform for noncompact symmetric spaces of the complex type | | Brian C. Hall
; Jeffrey J. Mitchell
; | | Date: |
17 Sep 2004 | | Subject: | Quantum Physics; Mathematical Physics; Differential Geometry | quant-ph math-ph math.DG 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. | | Source: | arXiv, quant-ph/0409118 | | Services: | Forum | Review | PDF | Favorites | |
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