Unbounded Self-Adjoint Operators on Hilbert Space
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Beschreibung
This textbook provides a modern account of the theory of unbounded self‑adjoint operators on Hilbert spaces and their spectral theory, with emphasis on applications in mathematical physics (Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm–Liouville operators, and the Hamburger moment problem). The new edition has been thoroughly revised and updated and features an extensive treatment of the self‑adjoint extension theory of symmetric operators. In addition, a number of advanced special topics are presented at the textbook level, accompanied by numerous illustrative examples and exercises.
The main themes of the book are:
- Basics of unbounded operators and fundamental self‑adjointness criteria
- Spectral integrals, spectral theorems, and functional calculus for self‑adjoint and normal operators
- Perturbations of self‑adjointness and of the spectra of self‑adjoint operators
- Forms and operators
- Boundary triplets
- The Krein transform and the Krein–Vishik–Birman theory of positive self‑adjoint extensions
With several updates and additions, this edition further enhances an established standard reference and accessible entry point to the subject.
This textbook provides a modern account of the theory of unbounded self‑adjoint operators on Hilbert spaces and their spectral theory, with emphasis on applications in mathematical physics (Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm–Liouville operators, and the Hamburger moment problem). The new edition has been thoroughly revised and updated and features an extensive treatment of the self‑adjoint extension theory of symmetric operators. In addition, a number of advanced special topics are presented at the textbook level, accompanied by numerous illustrative examples and exercises.
The main themes of the book are:
- Basics of unbounded operators and fundamental self‑adjointness criteria
- Spectral integrals, spectral theorems, and functional calculus for self‑adjoint and normal operators
- Perturbations of self‑adjointness and of the spectra of self‑adjoint operators
- Forms and operators
- Boundary triplets
- The Krein transform and the Krein–Vishik–Birman theory of positive self‑adjoint extensions
With several updates and additions, this edition further enhances an established standard reference and accessible entry point to the subject.
Treats unbounded self-adjoint operators with emphasis on applications in mathematical physics Introduces several important topics not usually covered in textbooks The new edition includes additional advanced topics on unbounded operators
Autor*in
Konrad Schmüdgen
Themen in »Unbounded Self-Adjoint Operators on Hilbert Space«
Banach space Hamburger moment problem Hilbert space Perturbation of self-adjointness Schrödinger operators Self-adjoint extension theory Self-adjoint operators Spectral theory Sturm-Liouville operators Cayley transform Krein transform Boundary triplets