CHAPTER Ⅰ ABSTRACT HILBERT SPACE AND ITS REALIZATIONS

1．The Concept of Space

2．Abstract Hilbert Space

3．Abstract Unitary Spaces

4．Linear Manifolds in Hilbert Space

5．Realizations of Abstract Hilbert Space

CHAPTER Ⅱ TRANSFORMATIONS IN HILBERT SPACE

1．Linear Transformations

2．Symmetric Transformations

3．Bounded Linear Transformations

4．Projections

5．Isometric and Unitary Transformations

6．Unitary Invariance

CHAPTER Ⅲ EXAMPLES OF LINEAR TRANSFORMATIONS

1．Infinite Matrices

2．Integral Operators

3．Differential Operators

4．Operators of Other Types

CHAPTER Ⅳ RESOLVENTS,SPECTRA,REDUCIBILITY

1．The Fundamental Problems

2．Resolvents and Spectra

8．Reducibility

CHAPTER Ⅴ SELF-ADJOINT TRANSFORMATIONS

1．Analytical Methods

2．Analytical Representation of the Resolvent

3．The Reducibility of the Resolvent

4．The Analytical Representation of a Self-Adjoint Transformation

5．The Spectrum of a Self-Adjoint Transformation

CHAPTER Ⅵ THE OPERATIONAL CALCULUS

1．The Radon-Stieltjes Integral

2．The Operational Calculus

CHAPTER Ⅶ THE UNITARY EQUIVALENCE OF SELF-ADJOINT TRANSFORMATIONS

1．Preparatory Theorems

2．Unitary Equivalence

3．Self-Adjoint Transformations with Simple Spectra

4．The Reducibility of Self-Adjoint Transformations

5．Reduction to Principal Axes

CHAPTER Ⅷ GENERAL TYPES OF LINEAR TRANSFORMATIONS

1．Permutability

2．Unitary Transformations

3．Normal Transformations

4．A Theorem on Factorization

CHAPTER Ⅸ SYMMETRIC TRANSFORMATIONS

1．The General Theory

2．Real Transformations

3．Approximation Theorems

CHAPTER Ⅹ APPLICATIONS

1．Integral Operators

2．Ordinary Differential Operators of the First Order

3．Ordinary Differential Operators of the Second Order

4．Jacobi Matrices and Allied Topics

Index