Sturm-Liouville theory
Sturm-Liouville theory
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DOI：
10.1090/surv/121
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
A. Zettl
中科院分区：
文献类型：
--
作者：
A. Zettl
在1836年至1837年斯特姆和刘维发表了一系列文件，二阶线性常微分算子，这开始了主题现在被称为斯特姆刘维问题。赫尔曼魏尔在1910年发表了一篇文章，开始研究奇异的Sturm-Liouville问题。从那时起，Sturm-Liouville理论仍然是一个非常活跃的研究领域，在数学和数学物理中有许多应用。本书的目的是（a）提供一个现代调查的一些基本性质的斯特姆刘维理论和（B）使读者的前沿知识的某些方面，这一理论。要使用这本书，只有一个基本的知识，先进的微积分和一个基本的知识勒贝格积分和算子理论的假设。提供了广泛的参考文献和例子，并给出了许多开放的问题。这些例子包括与贝塞尔、傅立叶、休恩、因斯、雅可比、约根斯、拉茨科、勒让德、利特尔伍德-麦克劳德、马蒂厄、迈斯纳、莫尔斯的名字有关的经典方程和函数，以及与谐振子和氢原子有关的例子。应用数学和数学物理的许多特殊功能出现在这些例子中。
In 1836-1837 Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which started the subject now known as the Sturm-Liouville problem. In 1910 Hermann Weyl published an article which started the study of singular Sturm-Liouville problems. Since then, the Sturm-Liouville theory remains an intensely active field of research, with many applications in mathematics and mathematical physics. The purpose of the present book is (a) to provide a modern survey of some of the basic properties of Sturm-Liouville theory and (b) to bring the reader to the forefront of knowledge about some aspects of this theory. To use the book, only a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory are assumed. An extensive list of references and examples is provided and numerous open problems are given. The list of examples includes those classical equations and functions associated with the names of Bessel, Fourier, Heun, Ince, Jacobi, Jorgens, Latzko, Legendre, Littlewood-McLeod, Mathieu, Meissner, Morse, as well as examples associated with the harmonic oscillator and the hydrogen atom. Many special functions of applied mathematics and mathematical physics occur in these examples.