Ebook: Unbounded Self-adjoint Operators on Hilbert Space

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

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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