Support theorems for the spherical Radon transform on manifolds

Let M be a real-analytic manifold and let S ⊂ M be a real-analytic hypersurface. We prove local support theorems for the spherical Radon transform that integrates over spheres centered at points on S. Our theorems are valid for a broad class of distributions with initial support restrictions dependi...

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Bibliographic Details
Published in:International Mathematics Research Notices 2006, Vol.2006
Main Author: Quinto, E. T.
Format: Article
Language:English
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Summary:Let M be a real-analytic manifold and let S ⊂ M be a real-analytic hypersurface. We prove local support theorems for the spherical Radon transform that integrates over spheres centered at points on S. Our theorems are valid for a broad class of distributions with initial support restrictions depending on S and the injectivity radius of M. The proofs involve the microlocal analysis of the sphere transform and a microlocal Holmgren theorem of Kawai, Kashiwara, and Hörmander.
ISSN:1073-7928
1687-1197
1687-0247
DOI:10.1155/IMRN/2006/67205