An Introduction to Linear Transformations in Hilbert Space

, by Murray, F. J.

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ISBN: 9780691095691 | 0691095698
Cover: Paperback
Copyright: 12/31/1941

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Supplemental Materials

Preface

Table of Contents

Introduction

(3)

Hilbert Space

(18)

The Postulates

(2)

Linear Normed Spaces

(1)

Additivity and Continuity

(4)

Linear Functionals

(3)

Linear Manifolds

(2)

Orthonormal Sets

(6)

Realizations of Hilbert Space

(9)

Preliminary Considerations

(1)

(3)

h1 hn and h1 h2

(1)

(4)

Additive and Closed Transformations

(14)

The Graph of a Transformation

(3)

Adjoints and Closure

(4)

Symmetric and Self-adjoint Operators

(4)

C.a.d.d. Transformations

(3)

Weak Convergence

(6)

Weak Completeness

(2)

Weak Compactness

(1)

Closed Transformations with Domain h

(3)

Projections and Isometry

(13)

Projections

(5)

Unitary and Isometric Transformations

(4)

Partially Isometric Transformations

(2)

C.a.d.d. Operators

(2)

Resolutions of the Identity

(17)

Self-adjoint Transformations with H Finite Dimensional

(3)

Resolutions of the Identity and Integration

(6)

Improper Integrals

(4)

Commutativity and Normal Operators

(4)

Bounded Self-Adjoint and Unitary Transformations

(14)

Functions of a Bounded H

(4)

(Hf, g)

(3)

Integral Representation of a bounded H

(1)

Integral Representation of a Unitary Operator

(6)

Canonical Resolution and Integral Representations

(15)

The Canonical Resolution

(5)

Self-adjoint Operators

100

(2)

Normal Operators

102

(8)

Symmetric Operators

110

(12)

The Cayley Transform

110

(6)

Structure and Existence of Maximal Symmetric Operators

116

(6)

References to Further Developments

122

(8)

Spectrum

122

(1)

Operational Calculus

123

(1)

Commutativity and Normal Operators

124

(1)

Symmetric Transformations

125

(1)

Infinite Matrices

125

(1)

Operators of Finite Norms

126

Stone's Theorem

125

(2)

Rings of Operators

127

(3)

References to Applications

130

Integral and Other Types of Operators

130

Differential Operators

130

Quantum Mechanics

131

Classical Mechanics

131

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An Introduction to Linear Transformations in Hilbert Space

Table of Contents

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