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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}}$.

References [Enhancements On Off] (What's this?)

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Keywords: Surface carried measure, Fourier transform, zero set
Article copyright: © Copyright 1993 American Mathematical Society

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