Fourier transform and rigidity of certain distributions

الأصل · EN

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.