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Operator Theory: Advances and Applications

Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications

Authors: Möller, Manfred, Pivovarchik, Vyacheslav

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  • Provides comprehensive information on the spectral properties of quadratic operator pencils
  • Includes a detailed discussion of applications to spectral problems from physics and engineering
  • Presents a thorough investigation of the connection between the spectral properties of quadratic operator pencils and generalized Hermite-Biehler functions
  • Many of the results presented have never before been published in a monograph
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eBook $99.00
price for USA in USD (gross)
  • ISBN 978-3-319-17070-1
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  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-319-17069-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: November 4, 2016
  • ISBN 978-3-319-37567-0
  • Free shipping for individuals worldwide
About this book

The theoretical part of this monograph examines the distribution of the spectrum of operator polynomials, focusing on quadratic operator polynomials with discrete spectra. The second part is devoted to applications. Standard spectral problems in Hilbert spaces are of the form A-λI for an operator A, and self-adjoint operators are of particular interest and importance, both theoretically and in terms of applications. A characteristic feature of self-adjoint operators is that their spectra are real, and many spectral problems in theoretical physics and engineering can be described by using them. However, a large class of problems, in particular vibration problems with boundary conditions depending on the spectral parameter, are represented by operator polynomials that are quadratic in the eigenvalue parameter and whose coefficients are self-adjoint operators. The spectra of such operator polynomials are in general no more real, but still exhibit certain patterns. The distribution of these spectra is the main focus of the present volume. For some classes of quadratic operator polynomials, inverse problems are also considered. The connection between the spectra of such quadratic operator polynomials and generalized Hermite-Biehler functions is discussed in detail.

Many applications are thoroughly investigated, such as the Regge problem and damped vibrations of smooth strings, Stieltjes strings, beams, star graphs of strings and quantum graphs. Some chapters summarize advanced background material, which is supplemented with detailed proofs. With regard to the reader’s background knowledge, only the basic properties of operators in Hilbert spaces and well-known results from complex analysis are assumed.

Reviews

“In this monograph the authors study spectral properties of polynomial operator pencils … . Large number so applications is an important feature of the book, and makes it highly useful for researchers interested in diverse problem of applied mathematics. … The book is highly readable and the presentation is mathematically rigorous.” (Ivica Nakić, Mathematical Reviews, July, 2016)


Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $99.00
price for USA in USD (gross)
  • ISBN 978-3-319-17070-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-319-17069-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: November 4, 2016
  • ISBN 978-3-319-37567-0
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
246
Copyright
2015
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-17070-1
DOI
10.1007/978-3-319-17070-1
Hardcover ISBN
978-3-319-17069-5
Softcover ISBN
978-3-319-37567-0
Series ISSN
0255-0156
Edition Number
1
Number of Pages
XVII, 412
Number of Illustrations
11 b/w illustrations
Topics