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LINEAR TRANSFORMATIONS IN HILBERT SPACE AND THEIR APPLICATIONS TO ANALYSIS
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  • 出版时间：1932
  • 标注页数：622页
  • 文件大小：21MB
  • 文件页数：630页
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图书目录

CHAPTER Ⅰ ABSTRACT HILBERT SPACE AND ITS REALIZATIONS1

1．The Concept of Space1

2．Abstract Hilbert Space2

3．Abstract Unitary Spaces16

4．Linear Manifolds in Hilbert Space18

5．Realizations of Abstract Hilbert Space23

CHAPTER Ⅱ TRANSFORMATIONS IN HILBERT SPACE33

1．Linear Transformations33

2．Symmetric Transformations49

3．Bounded Linear Transformations53

4．Projections70

5．Isometric and Unitary Transformations76

6．Unitary Invariance83

CHAPTER Ⅲ EXAMPLES OF LINEAR TRANSFORMATIONS86

1．Infinite Matrices86

2．Integral Operators98

3．Differential Operators112

4．Operators of Other Types124

CHAPTER Ⅳ RESOLVENTS,SPECTRA,REDUCIBILITY125

1．The Fundamental Problems125

2．Resolvents and Spectra128

8．Reducibility150

CHAPTER Ⅴ SELF-ADJOINT TRANSFORMATIONS155

1．Analytical Methods155

2．Analytical Representation of the Resolvent165

3．The Reducibility of the Resolvent172

4．The Analytical Representation of a Self-Adjoint Transformation180

5．The Spectrum of a Self-Adjoint Transformation184

CHAPTER Ⅵ THE OPERATIONAL CALCULUS198

1．The Radon-Stieltjes Integral198

2．The Operational Calculus221

CHAPTER Ⅶ THE UNITARY EQUIVALENCE OF SELF-ADJOINT TRANSFORMATIONS242

1．Preparatory Theorems242

2．Unitary Equivalence247

3．Self-Adjoint Transformations with Simple Spectra275

4．The Reducibility of Self-Adjoint Transformations288

5．Reduction to Principal Axes294

CHAPTER Ⅷ GENERAL TYPES OF LINEAR TRANSFORMATIONS299

1．Permutability299

2．Unitary Transformations302

3．Normal Transformations311

4．A Theorem on Factorization331

CHAPTER Ⅸ SYMMETRIC TRANSFORMATIONS334

1．The General Theory334

2．Real Transformations357

3．Approximation Theorems365

CHAPTER Ⅹ APPLICATIONS397

1．Integral Operators397

2．Ordinary Differential Operators of the First Order424

3．Ordinary Differential Operators of the Second Order448

4．Jacobi Matrices and Allied Topics530

Index615

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