Frame expansions of test functions, tempered distributions, and ultradistributions (Q2327046)

The authors first review some known results concerning series expansions in Fréchet spaces based on the theory of (general) Fréchet frames as developed in [\textit{S. Pilipović} and \textit{D. T. Stoeva}, Anal. Appl., Singap. 12, No. 2, 195--208 (2014; Zbl 1290.42058)]. New results on series expansions of tempered distributions and ultradistributions are presented in Section~4, based on a general result concerning frames localized with respect to a Riesz basis. The results are presented without proofs, which will appear elsewhere. For the entire collection see [Zbl 1415.35004].