On the Moment Problem in the Spaces of Ultradifferentiable Functions of Mean Type

被引：0
作者：
D. A. Polyakova
机构：
[1] Southern Federal University,
[2] Southern Mathematical Institute of Vladikavkaz Scientific Center of the Russian Academy of Sciences,undefined
来源：
Siberian Mathematical Journal | 2022年 / 63卷
关键词：
ultradifferentiable function; moment problem; Borel map; 517.518;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider a version of the classical moment problem in the Beurling and Roumieu spaces of ultradifferentiable functions of mean type on the real axis. We obtain the necessary and sufficient conditions for the weights \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \omega $\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \sigma $\end{document} under which, for each number sequence in the space generated by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \sigma $\end{document}, there is an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \omega $\end{document}-ultradifferentiable function whose derivatives at zero coincide with the elements of the sequence.
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页码：336 / 347
页数：11
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