Overview
- 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
Part of the book series: Graduate Texts in Mathematics (GTM, volume 265)
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Table of contents (16 chapters)
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Front Matter
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Basics of Closed Operators
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Front Matter
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Spectral Theory
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Front Matter
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Special Topics
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Front Matter
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Perturbations of Self-adjointness and Spectra
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Front Matter
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Forms and Operators
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Front Matter
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Self-adjoint Extension Theory of Symmetric Operators
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Front Matter
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Keywords
About this book
- 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
Reviews
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)
Authors and Affiliations
Bibliographic Information
Book Title: Unbounded Self-adjoint Operators on Hilbert Space
Authors: Konrad Schmüdgen
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-94-007-4753-1
Publisher: Springer Dordrecht
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media Dordrecht 2012
Hardcover ISBN: 978-94-007-4752-4Published: 07 July 2012
Softcover ISBN: 978-94-007-9741-3Published: 09 August 2014
eBook ISBN: 978-94-007-4753-1Published: 09 July 2012
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XX, 432
Topics: Functional Analysis, Mathematical Methods in Physics, Operator Theory, Mathematical Physics, Theoretical, Mathematical and Computational Physics