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- W2022953171 abstract "Abstract When n > 2 it is well known that the spherical partial sums of n -fold Fourier integrals of the characteristic function of a ball diverge at the origin, because of the jump at the boundary of the ball. The relation between convergence properties of spherical partial sums and geometry of discontinuities of the function being expanded was investigated in the well-known paper of Kahane. The most remarkable result, proved by Kahane in this paper, asserts that for the characteristic function of a bounded domain in R 3 the inverse statement is also true: if the surface is analytic and if the spherical Fourier inversion fails at a single point, then the surface must be a sphere and the point must be the center. In this Note we consider nonspherical partial sums, i.e. Fourier integrals under summation over smoothly bounded strongly convex symmetric sets and prove the natural generalization of the Kahane theorem." @default.
- W2022953171 created "2016-06-24" @default.
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- W2022953171 date "2010-10-01" @default.
- W2022953171 modified "2023-09-27" @default.
- W2022953171 title "The Kahane theorem for nonspherical partial sums of Fourier integrals" @default.
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- W2022953171 doi "https://doi.org/10.1016/j.crma.2010.07.029" @default.
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