Graduate Texts in Mathematics

Unbounded Self-adjoint Operators on Hilbert Space

Authors: Schmüdgen, Konrad

  • 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
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  • ISBN 978-94-007-4753-1
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Hardcover $79.95
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  • ISBN 978-94-007-4752-4
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  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
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  • ISBN 978-94-007-9741-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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About this Textbook

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

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)


Table of contents (16 chapters)

  • Closed and Adjoint Operators

    Schmüdgen, Konrad

    Pages 3-23

  • The Spectrum of a Closed Operator

    Schmüdgen, Konrad

    Pages 25-36

  • Some Classes of Unbounded Operators

    Schmüdgen, Konrad

    Pages 37-57

  • Spectral Measures and Spectral Integrals

    Schmüdgen, Konrad

    Pages 61-84

  • Spectral Decompositions of Self-adjoint and Normal Operators

    Schmüdgen, Konrad

    Pages 85-114

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-94-007-4753-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-94-007-4752-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-94-007-9741-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Unbounded Self-adjoint Operators on Hilbert Space
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
265
Copyright
2012
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-007-4753-1
DOI
10.1007/978-94-007-4753-1
Hardcover ISBN
978-94-007-4752-4
Softcover ISBN
978-94-007-9741-3
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XX, 432
Topics