General Stieltjes moment problems for rapidly decreasing smooth functions

Ricardo Estrada ¹   ; Jasson Vindas ²

¹ Department of Mathematics Louisiana State University Baton Rouge, LA 70803, U.S.A.
² Department of Mathematics Ghent University Krijgslaan 281 B-9000 Gent, Belgium

Studia Mathematica, Tome 238 (2017) no. 3, pp. 271-295

Résumé

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.

Détail

DOI : 10.4064/sm8728-3-2017

Keywords: necessary sufficient conditions sequence infty functions under which every generalized stieltjes moment problem int infty phi quad mathbb has solutions phi mathcal mathbb operatorname supp phi subseteq infty furthermore consider general problems kind measure distribution sequences infty study vector moment problems values chet spaces multidimensional moment problems