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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The null set of the Fourier transform for a surface carried measure


Author: Li Min Sun
Journal: Proc. Amer. Math. Soc. 118 (1993), 1107-1112
MSC: Primary 42B10; Secondary 42B25
MathSciNet review: 1137235
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Abstract: Let $ du$ be a smooth positive measure carried by a smooth compact hypersurface $ S$ that is strictly convex and without boundary in $ {R^n}(n \geqslant 2)$. Assume that both $ S$ and $ du$ are symmetric about the origin. If $ \hat du$ denotes the Fourier transform of $ du$ then we show that the null set of $ \hat du$ is a disjoint union of a compact set and countably many hypersurfaces that are all diffeomorphic to the unit sphere $ {S^{n - 1}}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1137235-5
PII: S 0002-9939(1993)1137235-5
Keywords: Surface carried measure, Fourier transform, zero set
Article copyright: © Copyright 1993 American Mathematical Society