{"title":"Titchmarsh-Weyl m-系数的数值确定及其在HELP不等式中的应用","authors":"B. M. Brown, V. Kirby, J. Pryce","doi":"10.1098/rspa.1989.0122","DOIUrl":null,"url":null,"abstract":"This paper is concerned with numerical methods for finding m(λ), the Titchmarsh-Weyl m-coefficient, for the singular eigenvalue equation -y\" + qy = λy on [0, ∞) and the results are applied to the problem of finding best constants for Everitt’s extension to the Hardy-Little-wood-Pόlya (HELP) integral inequality.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"10 1","pages":"167 - 188"},"PeriodicalIF":0.0000,"publicationDate":"1989-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"15","resultStr":"{\"title\":\"Numerical determination of the Titchmarsh-Weyl m-coefficient and its applications to HELP inequalities\",\"authors\":\"B. M. Brown, V. Kirby, J. Pryce\",\"doi\":\"10.1098/rspa.1989.0122\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is concerned with numerical methods for finding m(λ), the Titchmarsh-Weyl m-coefficient, for the singular eigenvalue equation -y\\\" + qy = λy on [0, ∞) and the results are applied to the problem of finding best constants for Everitt’s extension to the Hardy-Little-wood-Pόlya (HELP) integral inequality.\",\"PeriodicalId\":20605,\"journal\":{\"name\":\"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences\",\"volume\":\"10 1\",\"pages\":\"167 - 188\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1989-11-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1098/rspa.1989.0122\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rspa.1989.0122","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 15
摘要
本文研究了奇异特征值方程-y”+ qy = λy在[0，∞]上求Titchmarsh-Weyl m系数m(λ)的数值方法，并将所得结果应用于求Everitt对hardy - little -wood- p lya (HELP)积分不等式的推广的最佳常数问题。
Numerical determination of the Titchmarsh-Weyl m-coefficient and its applications to HELP inequalities
This paper is concerned with numerical methods for finding m(λ), the Titchmarsh-Weyl m-coefficient, for the singular eigenvalue equation -y" + qy = λy on [0, ∞) and the results are applied to the problem of finding best constants for Everitt’s extension to the Hardy-Little-wood-Pόlya (HELP) integral inequality.
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