دانلود کتاب An Introduction to Linear Transformations in Hilbert Space. (AM-4), Volume 4

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TABLE OF CONTENTS\nPreface\nChapter I. INTRODUCTION\nChapter II. HILBERT SPACE\n §1. The Postulates\n §2. Linear Normed Spaces\n §3. Additivity and Continuity\n §4. Linear Functionals\n §5. Linear Manifolds\n §6. Orthonormal Sets\nChapter III. REALIZATIONS OF HILBERT SPACE\n §1. Preliminary Considerations\n §2. l2\n §3. h1 ⊕ ... ⊕ hn and h1 ⊕ h2 ⊕ ...\n §4. L2\nChapter IV. ADDITIVE AND CLOSED TRANSFORMATIONS\n §1. The Graph of a Transformation\n §2. Adjoints and Closure\n §3. Symmetric and Self-adjoint Operators\n §4. C.a.d.d. Transformations\nChapter V. WEAK CONVERGENCE\n §1. Weak Completeness\n §2. Weak Compactness\n §3. Closed Transformations with Domain h\nChapter VI. PROJECTIONS AND ISOMETRY\n §1. Projections\n §2. Unitary and Isometric Transformations\n §3. Partially Isometric Transformations\n §4. C.a.d.d. Operators\nChapter VII. RESOLUTIONS OF THE IDENTITY\n §1. Self-adjoint Transformations with H Finite Dimensional\n §2. Resolutions of the Identity and Integration\n §3. Improper Integrals\n §4. Commutativity and Normal Operators\nChapter VIII. BOUNDED SELF-ADJOINT AND UNITARY TRANSFORMATIONS\n §1. Functions of a Bounded H\n §2. (Hf,g)\n §3. Integral Representation of a bounded H\n §4. Integral Representation of a Unitary Operator\nChapter IX. CANONICAL RESOLUTION AND INTEGRAL REPRESENTATIONS\n §1. The Canonical Resolution\n §2. Self-adjoint Operators\n §3. Normal Operators\nChapter X. SYMMETRIC OPERATORS\n §1. The Cayley Transform\n §2. Structure and Existence of Maximal Symmetric Operators\nChapter XI. REFERENCES TO FURTHER DEVELOPMENTS\n §1. Spectrum\n §2. Operational Calculus\n §3. Commutativity and Normal Operators\n §4. Symmetric Transformations\n §5. Infinite Matrices\n §6. Operators of Finite Norms\n §7. Stone’ s Theorem\n §8. Rings of Operators\nChapter XII. REFERENCES TO APPLICATIONS\n §1. Integral and Other Types of Operators\n §2. Differential Operators\n §3. Quantum Mechanics\n §4. Classical Mechanics