Frame expansions of test functions, tempered distributions, and ultradistributions

Abstract

The paper is devoted to frame expansions in Fréchet spaces. First we review some results which concern series expansions in general Fréchet spaces via Fréchet and General Fréchet frames. Then we present some new results on series expansions of tempered distributions and ultradistributions, and the corresponding test functions, via localized frames and coefficients in appropriate sequence spaces.

References in corpus (1)

• Eigenfunction expansions of ultradifferentiable functions and ultradistributions in ${\mathbb{R}}^n$