Sturm-Liouville Operator Functions

IF 1.5 3区数学 Q1 MATHEMATICS

Dissertationes Mathematicae Pub Date : 2018-01-01 DOI:10.4064/DM763-3-2018

Felix Früchtl

引用次数: 1

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.

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Sturm-Liouville算子函数

许多特殊函数是微分方程和泛函方程的解。我们利用这一对偶性求解了一大类抽象Sturm-Liouville方程，建立了Sturm-Liouville算子函数理论;余弦、贝塞尔和勒让德算子函数作为特殊情况包含。这是算子函数与包含(超)群的所有表示的超群的卷积相乘的一般概念的一部分，并进一步抽象了柯西问题。

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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来源期刊

Dissertationes Mathematicae 数学-数学

CiteScore

2.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： 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.