{"title":"Sturm-Liouville算子函数","authors":"Felix Früchtl","doi":"10.4064/DM763-3-2018","DOIUrl":null,"url":null,"abstract":"Many special functions are solutions of both, a differential and a functional equation. We use this duality to solve a large class of abstract Sturm-Liouville equations, initiating a theory of Sturm-Liouville operator functions; cosine, Bessel, and Legendre operator functions are contained as special cases. This is part of a general concept of operator functions being multiplicative with respect to convolution of a hypergroup - containing all representations of (hyper)groups, and further abstract Cauchy problems.","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":"532 1","pages":"1-52"},"PeriodicalIF":1.5000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Sturm-Liouville Operator Functions\",\"authors\":\"Felix Früchtl\",\"doi\":\"10.4064/DM763-3-2018\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Many special functions are solutions of both, a differential and a functional equation. We use this duality to solve a large class of abstract Sturm-Liouville equations, initiating a theory of Sturm-Liouville operator functions; cosine, Bessel, and Legendre operator functions are contained as special cases. This is part of a general concept of operator functions being multiplicative with respect to convolution of a hypergroup - containing all representations of (hyper)groups, and further abstract Cauchy problems.\",\"PeriodicalId\":51016,\"journal\":{\"name\":\"Dissertationes Mathematicae\",\"volume\":\"532 1\",\"pages\":\"1-52\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dissertationes Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/DM763-3-2018\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dissertationes Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/DM763-3-2018","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Many special functions are solutions of both, a differential and a functional equation. We use this duality to solve a large class of abstract Sturm-Liouville equations, initiating a theory of Sturm-Liouville operator functions; cosine, Bessel, and Legendre operator functions are contained as special cases. This is part of a general concept of operator functions being multiplicative with respect to convolution of a hypergroup - containing all representations of (hyper)groups, and further abstract Cauchy problems.
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DISSERTATIONES MATHEMATICAE publishes long research papers (preferably 50-100 pages) in any area of mathematics. An important feature of papers accepted for publication should be their utility for a broad readership of specialists in the domain. In particular, the papers should be to some reasonable extent self-contained. The paper version is considered as primary.
The following criteria are taken into account in the reviewing procedure: correctness, mathematical level, mathematical novelty, utility for a broad readership of specialists in the domain, language and editorial aspects. The Editors have adopted appropriate procedures to avoid ghostwriting and guest authorship.
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