Fourier transform and rigidity of certain distributions

Abstract

Let E be a finite-dimensional vector space over a local field, and F be its dual. For a closed subset X of E, and Y of F, consider the space D -ξ(E; X, Y) of tempered distributions on E whose support are contained in X and support of whose Fourier transform are contained in Y. We show that D-ξ(E; X, Y) possesses a certain rigidity property, for X, Y which are some finite unions of affine subspaces. © World Scientific Publishing Company.