Hyers–Ulam Stability of the Coefficient Multipliers on Analytic Hilbert Spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-05-29 DOI:10.1007/s00009-024-02673-6

Chun Wang, Tian-Zhou Xu

引用次数: 0

Abstract

In this paper, we investigate the Hyers–Ulam stability of the coefficient multipliers on the Hardy space \(H^2\) and the Bergman space \(A^2\), meanwhile, we also investigate the Hyers–Ulam stability of the coefficient multipliers between the Bergman space \(A^2\) and the Hardy space \(H^2\). We give the necessary and sufficient condition for the coefficient multipliers to have the Hyers–Ulam stability on the Hardy space \(H^2\), on the Bergman space \(A^2\) and between the Bergman space \(A^2\) and the Hardy space \(H^2\), respectively. We also show that the best constant of Hyers–Ulam stability exists under different circumstances. Some results generalized the results of MacGregor and Zhu when \(p=2\) in MacGregor and Zhu article (Mathematika 42:413–426, 1995). Moreover, some illustrative examples are also discussed.

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解析希尔伯特空间上系数乘数的海尔-乌兰稳定性

本文研究了Hardy空间（H^2\ ）和Bergman空间（A^2\ ）上系数乘数的Hyers-Ulam稳定性，同时还研究了Bergman空间（A^2\ ）和Hardy空间（H^2\ ）之间系数乘数的Hyers-Ulam稳定性。我们分别给出了系数乘数在哈代空间（H^2\ ）、伯格曼空间（A^2\ ）以及伯格曼空间（A^2\ ）和哈代空间（H^2\ ）之间具有海尔斯-乌兰稳定性的必要条件和充分条件。我们还证明了在不同情况下存在海尔-乌兰稳定性的最佳常数。一些结果概括了 MacGregor 和 Zhu 文章（Mathematika 42:413-426, 1995）中 MacGregor 和 Zhu 在 \(p=2\) 时的结果。此外，还讨论了一些说明性的例子。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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