{"title":"解析希尔伯特空间上系数乘数的海尔-乌兰稳定性","authors":"Chun Wang, Tian-Zhou Xu","doi":"10.1007/s00009-024-02673-6","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we investigate the Hyers–Ulam stability of the coefficient multipliers on the Hardy space <span>\\(H^2\\)</span> and the Bergman space <span>\\(A^2\\)</span>, meanwhile, we also investigate the Hyers–Ulam stability of the coefficient multipliers between the Bergman space <span>\\(A^2\\)</span> and the Hardy space <span>\\(H^2\\)</span>. We give the necessary and sufficient condition for the coefficient multipliers to have the Hyers–Ulam stability on the Hardy space <span>\\(H^2\\)</span>, on the Bergman space <span>\\(A^2\\)</span> and between the Bergman space <span>\\(A^2\\)</span> and the Hardy space <span>\\(H^2\\)</span>, 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 <span>\\(p=2\\)</span> in MacGregor and Zhu article (Mathematika 42:413–426, 1995). Moreover, some illustrative examples are also discussed.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hyers–Ulam Stability of the Coefficient Multipliers on Analytic Hilbert Spaces\",\"authors\":\"Chun Wang, Tian-Zhou Xu\",\"doi\":\"10.1007/s00009-024-02673-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we investigate the Hyers–Ulam stability of the coefficient multipliers on the Hardy space <span>\\\\(H^2\\\\)</span> and the Bergman space <span>\\\\(A^2\\\\)</span>, meanwhile, we also investigate the Hyers–Ulam stability of the coefficient multipliers between the Bergman space <span>\\\\(A^2\\\\)</span> and the Hardy space <span>\\\\(H^2\\\\)</span>. We give the necessary and sufficient condition for the coefficient multipliers to have the Hyers–Ulam stability on the Hardy space <span>\\\\(H^2\\\\)</span>, on the Bergman space <span>\\\\(A^2\\\\)</span> and between the Bergman space <span>\\\\(A^2\\\\)</span> and the Hardy space <span>\\\\(H^2\\\\)</span>, 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 <span>\\\\(p=2\\\\)</span> in MacGregor and Zhu article (Mathematika 42:413–426, 1995). Moreover, some illustrative examples are also discussed.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-05-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00009-024-02673-6\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00009-024-02673-6","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Hyers–Ulam Stability of the Coefficient Multipliers on Analytic Hilbert Spaces
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.
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
