Unbounded Self-Adjoint Operators on Hilbert Space
(Sprache: Englisch)
This book explores unbounded self-adjoint operators on Hilbert space and their spectral theory, placing emphasis on applications in mathematical physics and analysis. Addresses advanced topics, and includes many examples and exercises.
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Produktinformationen zu „Unbounded Self-Adjoint Operators on Hilbert Space “
This book explores unbounded self-adjoint operators on Hilbert space and their spectral theory, placing emphasis on applications in mathematical physics and analysis. Addresses advanced topics, and includes many examples and exercises.
Klappentext zu „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
Inhaltsverzeichnis zu „Unbounded Self-Adjoint Operators on Hilbert Space “
I Basics onClosed Operators.- 1 Closed Operators and Adjoint Operators.- 2 Spectrum of Closed Operators.- 3 Some Classes of Unbounded Operators.- II Spectral Theory.- 4 Spectral Measures and Spectral Integrals.- 5 Spectral Decomposition of Selfadjoint and Normal Operators.- III Special Topics.- 6 One-Parameter Groups and Semigroups of Operators.- 7 Miscellaneous.- IV Petirbations of Selfadjointness and of Spectra of Selfadjoint Operators.- 8 Perturbations of Selfadjoint Operators.- 9 Trace Class Perturbations of Spectra of Selfadjoint Operators.- V Forms and Operators.- 10 Semibounded Forms and Selfadjoint Operators.- 11 Sectorial Forms and m-Sectorial Operators.- 12 Discrete Spectrum of Selfadjoint Operators.- VI Selfadjoint Extention Theory of Symmetric Operators.- 13 Selfajoint Extensions: Cayley Transform and Krein Transform.- 14 Selfadjoint Extensions: Boundary Triplets.- 15 Sturm-Liouville Operators.- One-Dimensional Moment Problem.
Autoren-Porträt von Konrad Schmüdgen
Schmuedgen is professor at the Mathematics Department of the University of Leipzig. Prof. Pavel Exner wrote about him: "In the eighties he was regarded at the Leipzig University as a rising star and the most gifted in the mathematical physics group".
Bibliographische Angaben
- Autor: Konrad Schmüdgen
- 2012, 2012, 432 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer Netherlands
- ISBN-10: 9400747527
- ISBN-13: 9789400747524
- Erscheinungsdatum: 07.07.2012
Sprache:
Englisch
Rezension 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)
"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)
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