A LOCAL UNIQUENESS THEOREM FOR WEIGHTED RADON TRANSFORMS

Abstract. We consider a weighted Radon transform in the plane, Rm(ξ, η) =R R f(x, ξx + η)m(x, ξ, η)dx, where m(x, ξ, η) is a smooth, positive function. Using an extension of an argument of Strichartz we prove a local injectivity theorem for Rm for essentially the same class of m(x, ξ, η) that was considered by Gindikin in his article in this issue. 1. Introduction. In the note [4] in this issue Simon Gindikin gives a new inversion formula for a class of weighted plane Radon transforms similar to the attenuated Radon transform. Gindikin’s proof is very short and uses no tools other than the fundamental theorem of calculus. Beginning with Novikov, [6], several authors have given similar results before using much more elaborate methods, in most cases base