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- 出版年份：1932
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CHAPTER Ⅰ ABSTRACT HILBERT SPACE AND ITS REALIZATIONS 1
1．The Concept of Space 1
2．Abstract Hilbert Space 2
3．Abstract Unitary Spaces 16
4．Linear Manifolds in Hilbert Space 18
5．Realizations of Abstract Hilbert Space 23
CHAPTER Ⅱ TRANSFORMATIONS IN HILBERT SPACE 33
1．Linear Transformations 33
2．Symmetric Transformations 49
3．Bounded Linear Transformations 53
4．Projections 70
5．Isometric and Unitary Transformations 76
6．Unitary Invariance 83
CHAPTER Ⅲ EXAMPLES OF LINEAR TRANSFORMATIONS 86
1．Infinite Matrices 86
2．Integral Operators 98
3．Differential Operators 112
4．Operators of Other Types 124
CHAPTER Ⅳ RESOLVENTS,SPECTRA,REDUCIBILITY 125
1．The Fundamental Problems 125
2．Resolvents and Spectra 128
8．Reducibility 150
CHAPTER Ⅴ SELF-ADJOINT TRANSFORMATIONS 155
1．Analytical Methods 155
2．Analytical Representation of the Resolvent 165
3．The Reducibility of the Resolvent 172
4．The Analytical Representation of a Self-Adjoint Transformation 180
5．The Spectrum of a Self-Adjoint Transformation 184
CHAPTER Ⅵ THE OPERATIONAL CALCULUS 198
1．The Radon-Stieltjes Integral 198
2．The Operational Calculus 221
CHAPTER Ⅶ THE UNITARY EQUIVALENCE OF SELF-ADJOINT TRANSFORMATIONS 242
1．Preparatory Theorems 242
2．Unitary Equivalence 247
3．Self-Adjoint Transformations with Simple Spectra 275
4．The Reducibility of Self-Adjoint Transformations 288
5．Reduction to Principal Axes 294
CHAPTER Ⅷ GENERAL TYPES OF LINEAR TRANSFORMATIONS 299
1．Permutability 299
2．Unitary Transformations 302
3．Normal Transformations 311
4．A Theorem on Factorization 331
CHAPTER Ⅸ SYMMETRIC TRANSFORMATIONS 334
1．The General Theory 334
2．Real Transformations 357
3．Approximation Theorems 365
CHAPTER Ⅹ APPLICATIONS 397
1．Integral Operators 397
2．Ordinary Differential Operators of the First Order 424
3．Ordinary Differential Operators of the Second Order 448
4．Jacobi Matrices and Allied Topics 530
Index 615