The Resource Spectral theory of operator pencils, Hermite-Biehler functions, and their applications, Manfred Möller, Vyacheslav Pivovarchik

Spectral theory of operator pencils, Hermite-Biehler functions, and their applications, Manfred Möller, Vyacheslav Pivovarchik

Label
Spectral theory of operator pencils, Hermite-Biehler functions, and their applications
Title
Spectral theory of operator pencils, Hermite-Biehler functions, and their applications
Statement of responsibility
Manfred Möller, Vyacheslav Pivovarchik
Creator
Contributor
Author
Subject
Genre
Language
eng
Summary
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-nI 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
Member of
Cataloging source
N$T
http://library.link/vocab/creatorName
Möller, Manfred
Dewey number
515.7222
Index
index present
LC call number
QC20.7.S64
LC item number
M65 2015eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Pivovarchik, Vyacheslav
Series statement
Operator theory: advances and applications
Series volume
v. 246
http://library.link/vocab/subjectName
  • Spectral theory (Mathematics)
  • Polynomial operator pencils
  • MATHEMATICS
  • MATHEMATICS
  • Polynomial operator pencils
  • Spectral theory (Mathematics)
Label
Spectral theory of operator pencils, Hermite-Biehler functions, and their applications, Manfred Möller, Vyacheslav Pivovarchik
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-17070-1
Instantiates
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- Part I: Operator Pencils -- 1. Quadratic Operator Pencils -- 2. Applications of Quadratic Operator Pencils -- 3. Operator Pencils with Essential Spectrum -- 4. Operator Pencils with a Gyroscopic Term -- Part II: Hermite-Biehler Functions -- 5. Generalized Hermite-Biehler Functions -- 6. Applications of Shifted Hermite-Biehler Functions -- Part III: Direct and Inverse Problems -- 7. Eigenvalue Asymptotics -- 8. Inverse Problems -- Part IV: Background Material -- 9. Spectral Dependence on a Parameter -- 10. Sobolev Spaces and Differential Operators -- 11. Analytic and Meromorphic Functions -- 12. Inverse Sturm-Liouville Problems -- Bibliography -- Index -- Index of Notation
Dimensions
unknown
Extent
1 online resource (xvii, 412 pages).
File format
unknown
Form of item
online
Isbn
9783319170695
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Other control number
10.1007/978-3-319-17070-1
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
Stock number
799076
System control number
  • (OCoLC)911032813
  • (OCoLC)ocn911032813
Label
Spectral theory of operator pencils, Hermite-Biehler functions, and their applications, Manfred Möller, Vyacheslav Pivovarchik
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-17070-1
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- Part I: Operator Pencils -- 1. Quadratic Operator Pencils -- 2. Applications of Quadratic Operator Pencils -- 3. Operator Pencils with Essential Spectrum -- 4. Operator Pencils with a Gyroscopic Term -- Part II: Hermite-Biehler Functions -- 5. Generalized Hermite-Biehler Functions -- 6. Applications of Shifted Hermite-Biehler Functions -- Part III: Direct and Inverse Problems -- 7. Eigenvalue Asymptotics -- 8. Inverse Problems -- Part IV: Background Material -- 9. Spectral Dependence on a Parameter -- 10. Sobolev Spaces and Differential Operators -- 11. Analytic and Meromorphic Functions -- 12. Inverse Sturm-Liouville Problems -- Bibliography -- Index -- Index of Notation
Dimensions
unknown
Extent
1 online resource (xvii, 412 pages).
File format
unknown
Form of item
online
Isbn
9783319170695
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Other control number
10.1007/978-3-319-17070-1
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
Stock number
799076
System control number
  • (OCoLC)911032813
  • (OCoLC)ocn911032813

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