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Pointwise Fourier Inversion on Rank One Symmetric Spaces and Related Topics

✍ Scribed by William O. Bray; Mark A. Pinsky

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 463 KB
Volume: 151
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1997.3146

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✦ Synopsis

This paper develops necessary and sufficient conditions for pointwise inversion of Fourier transforms on rank one symmetric spaces of non-compact type for functions in the piecewise smooth category. This extends results of Pinsky for isotropic Riemannian manifolds of constant curvature. Methodologically, a similar result on the Jacobi transform and a transplantation scheme from even dimensional spaces to certain odd dimensional real hyperbolic spaces naturally enter the picture.

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