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arXiv · 1609.07791

General Stieltjes moment problems for rapidly decreasing smooth functions

Ricardo Estrada·Jasson Vindas
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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 $ϕ\in\mathcal{S}(\mathbb{R})$ with $\operatorname*{supp} ϕ\subseteq[0,\infty)$. 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.

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Ricardo Estrada, Jasson Vindas. 2017-05-10. General Stieltjes moment problems for rapidly decreasing smooth functions. https://doi.org/10.4064/sm8728-3-2017

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