General Stieltjes moment problems for rapidly decreasing smooth functions
Volume 238 / 2017
Studia Mathematica 238 (2017), 271-295
MSC: Primary 30E05, 47A57, 44A60; Secondary 46F05.
DOI: 10.4064/sm8728-3-2017
Published online: 12 May 2017
Abstract
We give (necessary and sufficient) conditions on a sequence $\{ f_{n}\} _{n=0}^{\infty}$ of functions under which every generalized Stieltjes moment problem \[ \int_{0}^{\infty} f_{n}(x)\phi(x)\,{d} x=a_{n}, \ \quad n\in\mathbb{N}, \] has solutions $\phi\in\mathcal{S}(\mathbb{R})$ with $\operatorname{supp} \phi\subseteq[0,\infty)$. Furthermore, we consider more general problems of this kind for measure or distribution sequences $\{ f_{n}\} _{n=0}^{\infty}$. We also study vector moment problems with values in Fréchet spaces and multidimensional moment problems.
