A uniqueness result for the fourier transform of measures on the sphere

摘要

A finite measure supported by the unit sphere ~(n-1) in ? ~n and absolutely continuous with respect to the natural measure on ~(n-1) is entirely determined by the restriction of its Fourier transform to a sphere of radius r if and only 2πr is not a zero of any Bessel function J _(d+(n-2)/2) with d a nonnegative integer.