Perturbation theory for linear operators
Perturbation theory for linear operators
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DOI：
10.1007/978-3-662-12678-3
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发表时间：
1966
期刊：
影响因子：
--
通讯作者：
Tosio Kato
中科院分区：
文献类型：
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作者：
Tosio Kato
这本书是打算给一个线性算子的扰动理论的系统介绍。希望这本书将是有用的学生以及成熟的科学家，无论是在数学和物理science.Perturbation理论的线性算子是一个集合的多样化。的结果，在谱理论的线性算子，统一或多或少。松散的共同关心的行为，谱性质时，运营商经历了一个小的变化。自雷利和薛定谔创立以来，该理论在应用数学中占据了重要地位;在过去的几十年里，它已经发展成为一门有自己兴趣的数学学科。这本书的目的是在一个数学治疗的问题，适当考虑的应用。该理论的数学基础属于泛函分析。但是，由于这本书部分是为物理科学家准备的，他们可能缺乏泛函分析的训练，甚至没有预先假定该主题的元素。读者被假定只有线性代数和真实的和复分析的基本知识。功能分析中的必要工具，仅限于该主题的最基本部分，在需要时在文本中得到发展（第一章，第三章和第五章，第六章的部分）。在主要论述之前，有一个导言，其中包括对该理论的简要历史叙述。全文共分十章，每章都有一个总结。章分为节，节分为段。例如，I-§ 2.3指的是第一章第二节第三段;当在同一章和第二节中提及时，它只是写为§ 2.3。3当在同一节中提及时。定理，推论，引理，备注，问题和例子在每一节中都被编号为一个列表：定理2.1，推论2.2，引理2.3等。引理I-2.3指的是第一章的引理2.3，在同一章中它被简称为引理2.3。公式在每一节中连续编号; I-（2.3）是指第一章第二节的第三个公式，在同一章中称为（2.3）。有些问题是伪装的定理，并在书的后面部分引用。
This book is intended to give a systematic presentation of perturbation theory for linear operators. It is hoped that the book will be useful to students as well as to mature scientists, both in mathematics and in the physical sciences.Perturbation theory for linear operators is a collection of diversified. results in the spectral theory of linear operators, unified more or less. loosely by their common concern with the behavior of spectral properties when the operators undergo a small change. Since its creation by RAYLEIGH and SCHRÖDINGER, the theory has occupied an important place in applied mathematics; during the last decades, it has grown into a mathematical discipline with its own interest. The book aims at a mathematical treatment of the subject, with due consideration of applications. The mathematical foundations of the theory belong to functional analysis. But since the book is partly intended for physical scientists, who might lack training in functional analysis, not even the elements of that subject are presupposed. The reader is assumed to have only a basic knowledge of linear algebra and real and complex analysis. The necessary tools in functional analysis, which are restricted to the most elementary part of the subject, are developed in the text as the need for them arises (Chapters I, III and parts of Chapters V, VI). An introduction, containing a brief historical account of the theory, precedes the main exposition. There are ten chapters, each prefaced by a summary. Chapters are divided into sections, and sections into paragraphs. I-§ 2.3, for example, means paragraph three of section two of chapter one; it is simply written § 2.3 when referred to within the same chapter and par. 3 when referred to within the same section. Theorems, Corollaries, Lemmas, Remarks, Problems, and Examples are numbered in one list within each section: Theorem 2.1, Corollary 2.2, Lemma 2.3, etc. Lemma I-2.3 means Lemma 2.3 of chapter one, and it is referred to simply as Lemma 2.3 within the same chapter. Formulas are numbered consecutively within each section; I-(2.3) means the third formula of section two of chapter one, and it is referred to as (2.3) within the same chapter. Some of the problems are disguised theorems, and are quoted in later parts of the book.