哈恩-巴拿赫定理的应用、矩问题的解法及相关近似法

IF 2.3 3区数学 Q1 MATHEMATICS

Mathematics Pub Date : 2024-09-15 DOI:10.3390/math12182878

Octav Olteanu

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引用次数: 0

摘要

我们首先将 Krein-Milman 定理应用于完全单调函数的积分表示。文中还提到了凸优化的要素。接着，论文应用哈恩-巴纳奇（Hahn-Banach）型定理和多项式逼近法，得出了无界闭合区间上矩问题的最新结果。论文指出了解的存在性和唯一性的必要条件和充分条件。解决了算子值矩问题和标量值矩问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Applications of the Hahn-Banach Theorem, a Solution of the Moment Problem and the Related Approximation

We start by an application the of Krein–Milman theorem to the integral representation of completely monotonic functions. Elements of convex optimization are also mentioned. The paper continues with applications of Hahn–Banach-type theorems and polynomial approximation to obtain recent results on the moment problem on the unbounded closed interval . Necessary and sufficient conditions for the existence and uniqueness of the solution are pointed out. Operator-valued moment problems and a scalar-valued moment problem are solved.

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来源期刊

Mathematics Mathematics-General Mathematics

CiteScore

4.00

自引率

16.70%

发文量

4032

审稿时长

21.9 days

期刊介绍： Mathematics (ISSN 2227-7390) is an international, open access journal which provides an advanced forum for studies related to mathematical sciences. It devotes exclusively to the publication of high-quality reviews, regular research papers and short communications in all areas of pure and applied mathematics. Mathematics also publishes timely and thorough survey articles on current trends, new theoretical techniques, novel ideas and new mathematical tools in different branches of mathematics.