Sturm-Liouville Operator Functions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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

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.