A uniqueness result for the Fourier transform of measures on the paraboloid

Abstract

A finite measure supported by a paraboloid of revolution $\mathrm{\Sigma }$in ${\mathbb{R}}^3$ and absolutely continuous with respect to the naturalmeasure on $\mathrm{\Sigma }$ is entirely determined by the restriction ofits Fourier transform to a plane if and only if this plane is normalto the axis of $\mathrm{\Sigma }$.