The support of tempered distributions

Abstract

AbstractWe identify the support of a tempered distribution by evaluation of a sequence of test functions against the Fourier transform of the distribution. This improves previous results by removing the restriction that the distribution's Fourier transform be in $L^1_{loc}$ and be of polynomial growth. We use an apparently new technical lemma that implies that certain bounded approximate identities for $L^1(\R^n)$ are also topological approximate identities for elements of the space $\Sl$ of Schwartz functions.