Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

On the support of tempered distributions

Jasson Vindasa1 and Ricardo Estradaa1

a1 Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA, Email: (jvindas@math.lsu.edu, restrada@math.lsu.edu)

Abstract

We show that if the summability means in the Fourier inversion formula for a tempered distribution f xs2208 S′(xs211Dn) converge to zero pointwise in an open set Ω, and if those means are locally bounded in L1(Ω), then Ω xs2282 xs211Dn\supp f. We prove this for several summability procedures, in particular for Abel summability, Cesàro summability and Gauss-Weierstrass summability.

(Received January 12 2008)

Keywords

  • support of tempered distributions;
  • Fourier transforms;
  • Cesàro summability;
  • Abel summability;
  • spherical means

2000 Mathematics subject classification

  • Primary 42B10;
  • Secondary 46F10; 40C99