《線性運算元的微擾理論》是2016年世界圖書出版公司出版的著作，作者是Tosio、Kato 。
基本介紹
- 中文名：線性運算元的微擾理論
- 作者：Tosio、Kato
- 原作品：Perturbation Theory For Linear Operator
- 出版社： 世界圖書出版公司
- 出版時間：2016年05月01日
- 頁數：619 頁
- 開本：24 開
- 裝幀：平裝
- ISBN：9787519203184
內容簡介,圖書目錄,
內容簡介
《線性運算元的微擾理論（英文版）》系統地介紹了線性運算元微擾理論，收集了各種線性運算元譜理論，研究了運算元在微小變動的情況下，其譜特性的變動。《線性運算元的微擾理論（英文版）》凝聚了作者多年科研和教學成果，適用於科研工作者、高校教師和研究生。
圖書目錄
Introduchon
Chapter One Operator theory in finite—dimensional vector spaces
§1．Vector spaces and normed vector spaces
1．Basic nohons
2．Bases
3．Linear manifolds
4．Convergence and norms
5．Topological nohons in a normed space
6．Infinite series of vectors
7．Vector—valued funchons
§2．Linear forms and the adjoint space
1．Linear forms
2．The adjoint space
3．The adjoint basis
4．The adjoint space of a normed space
5．The convexity of balls
6．The second adjoint space
§3．Linear operators
1．Definihons．Matrix representations
2．Linear operations on operators
3．The algebra of linear operators
4．Projections．Nilpotents
5．Invariance．Decomposihon
6．The adjoint operator
§4．Analysis with operators
1．Convergence and norms for operators
2．The norm of T
3．Examples of norms
4．Infinte series of operators
5．Operator—valued functions
6．Pairs of projechons
§5．The eigenvalue problem
1．Definihons
2．The resolvent
3．Singularities of the resolvent
4．The canorucal form of an operator
5．The adjoint problem
6．Functions of an operator
7．Similarity transformations
§6．Operators in unitary spaces
1．Unitary spaces
2．The adjoint space
3．Orthonormal families
4．Linear operators
5．Symmetric forms and symmetric operators
6．Unitary，isometric and normal operators
7．Projections
8．Pairs of projections
9．The eigenvalue problem
10．The minimax principle
Chapter Two Perturbatlon theory in a finite—dimensional space
§1．Analyhc perturbahon of eigenvalues
1．The problem
2．Singularities of the eigenvalues
3．Perturbation of the resolvent
4．Perturbation of the eigenprojections
5．Singularities of the eigertprojections
6．Remarks and examples
7．The case of T（x） linear in x
8．Summary
§2．Perturbation series
1．The total projectin for the A—group
2．The weighted mean of eigenvalues
3．The reduction process
4．Formulas for higher approximahons
5．A theorem of MOTZKIN—TAUSSKY
6．The ranks of the coefficients of the perturbation series
§3．Convergence radu and error estimates
1．Simple estimates
2．The method of majorizing series
3．Estimates on eigenvectors
4．Further error eshmates
5．The special case of a normal unperturbed operator
6．The enumerahve method
§4．Similarity transformations of the eigenspaces and eigenvectors
1．Eigenvectors
2．Transformation funchons
3．Soluhon of the dffierential equahon
4．The transformation function and the reduction process
5．Simultaneous transformahon for several projections
6．Diagonalization of a holomorphic matrix function
§5．Non—analytic perturbations
1．Continuity of the eigenvalues and the total projechon
2．The numbering of the eigenvalues
3．Conhnuity of the eigenspaces and eigenvectors
4．Differentiability at a point
5．Differenhability in an interval
……
Chapter Three Introduction to the theory of operators in Banach spaces
Chapter Four Stability theorems
Chapter Five Operators in Hilbert spaces
Chapter Six Sesquilinear forms in Hilbert spaces and associated operators
Chapter Seven Analytic perturbation theory
Chapter Eight Asymptotic perturbation theory
Chapter Nine Perturbation theory for semigroups of operators
Chapter Ten Perturbauuon of continuous spectra and unitary equivalence
Supplementary Notes
