A UNIQUENESS RESULT FOR THE FOURIER TRANSFORM OF MEASURES ON THE SPHERE

Abstract

AbstractA finite measure supported by the unit sphere 𝕊n−1 in ℝn and absolutely continuous with respect to the natural measure on 𝕊n−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 Jd+(n−2)/2 with d a nonnegative integer.