General Stieltjes moment problems for rapidly decreasing smooth functions

Abstract

We give (necessary and sufficient) conditions over a sequence ${\left\{f_n\right\}}_{n=0}^{\infty }$ of functions under which every generalized Stieltjes moment problem \[ \int_{0}^{\infty} f_{n}(x)ϕ(x)\mathrm{d} x=a_{n}, \ \ \ n\in\mathbb{N}, \] has solutions $\varphi \in \mathcal{S}(\mathbb{R})$ with $\mathrm{supp}\varphi \subseteq [0,\infty )$. Furthermore, we consider more general problems of this kind for measure or distribution sequences ${\left\{f_n\right\}}_{n=0}^{\infty }$. We also study vector moment problems with values in Frechet spaces and multidimensional moment problems.

arXiv comment25 pages

Cited by in corpus (1)

• The vector-valued Stieltjes moment problem with general exponents