Description |
1 online resource |
Series |
Graduate texts in mathematics, 0072-5285 ; 265 |
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Graduate texts in mathematics ; 265.
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Contents |
Part 1. Basics of Closed Operators -- Closed and Adjoint Operators -- The Spectrum of a Closed Operator -- Some Classes of Unbounded Operators-- Part 2. Spectral Theory -- Spectral Measures and Spectral Integrals -- Spectral Decompositions of Self-adjoint and Normal Operators-- Part 3. Special Topics -- One-Parameter Groups and Semigroups of Operators -- Miscellanea-- Part 4. Perturbations of Self-Adjointness and Spectra -- Perturbations of Self-adjoint Operators -- Trace Class Perturbations of Spectra of Self-adjoint Operators-- Part 5. Forms and Operators -- Semibounded Forms and Self-adjoint Operators -- Sectorial Forms and m-Sectorial Operators -- Discrete Spectra of Self-adjoint Operators-- Part 6. Self-adjoint Extension Theory of Symmetric Operators -- Self-adjoint Extensions: Cayley Transform and Krein Transform -- Self-adjoint Extensions: Boundary Triplets -- Sturm-Liouville Operators -- The One-Dimensional Hamburger Moment Problem |
Summary |
The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger¡ operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics¡¡ are treated on a text book level¡ accompanied by numerous illustrating examples and exercises. The main themes of the book are the following: - Spectral integrals and¡ spectral decompositions of self-adjoint and normal operators - Perturbations of self-adjointness and of spectra of self-adjoint operators - Forms and operators - Self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extension |
Bibliography |
Includes bibliographical references and indexes |
Subject |
Operator theory.
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Hilbert space.
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Physics.
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Mathematics.
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Physics
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Mathematical Concepts
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Mathematics
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physics.
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MATHEMATICS -- Functional Analysis.
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Teoría de operadores
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Física
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Matemáticas
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Hilbert, Espacio de
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Physics
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Mathematics
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Hilbert space
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Operator theory
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Form |
Electronic book
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ISBN |
9789400747531 |
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9400747535 |
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9400747527 |
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9789400747524 |
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