Unbounded Self-adjoint Operators on Hilbert Space

Beschreibung

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
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
Includes important topics which are not yet or not completely presented in a text book Numerous well-choosen examples and exercises help the reader to learn dealing with unbounded operators Treats unbounded self-adjoint operators with the emphasis on applications in mathematical physics Includes supplementary material: sn.pub/extras Includes supplementary material: sn.pub/extras

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

Stimmen zu »Unbounded Self-adjoint Operators on Hilbert Space«

From the reviews:

“The book is devoted to the exposition of the theory of unbounded operators in the Hilbert space. … book starts with a standard introduction to the theory of closed and closable operators, with an explanation of the important difference between self-adjoint and symmetric operators. … Among the advantages of the book is the inclusion of a nice and voluminous selection of exercises. … the book can be used for teaching a graduate course in spectral theory to students in analysis and to physicists … .” (G. V. Rozenblum, Mathematical Reviews, January, 2013)

“I recommend the book as a reference for readers interested in the general theory of unbounded self-adjoint operators in Hilbert space. It is a valuable reference for numerous topics, including closed and adjoint operators, the general spectral theorem for self-adjoint operators, groups and semigroups of operators, semibounded and sectorial forms and their associated operators, and self-adjoint extensions of symmetric operators. … A special feature of the book is the inclusion of numerous examples based on multiplication operators and first and second order differential operators.” (Anton Zettl, SIAM Review, Vol. 55 (3), 2013)

“The book can be used for teaching a graduate course in spectral theory to students and is also suitable for self-study. The book consists of six parts, each of which is subdivided into several chapters, each chapter ending with a section containing exercises. … The book concludes with appendices devoted to basic topics in analysis and the theory of bounded operators.” (Michael Perelmuter, Zentralblatt MATH, Vol. 1257, 2013)

Details

Link teilen