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The Resource Spectral theory of operator pencils, HermiteBiehler functions, and their applications, Manfred Möller, Vyacheslav Pivovarchik
Spectral theory of operator pencils, HermiteBiehler functions, and their applications, Manfred Möller, Vyacheslav Pivovarchik
Resource Information
The item Spectral theory of operator pencils, HermiteBiehler functions, and their applications, Manfred Möller, Vyacheslav Pivovarchik represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Spectral theory of operator pencils, HermiteBiehler functions, and their applications, Manfred Möller, Vyacheslav Pivovarchik represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 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 AnI for an operator A, and selfadjoint operators are of particular interest and importance, both theoretically and in terms of applications. A characteristic feature of selfadjoint 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 selfadjoint 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 HermiteBiehler 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 wellknown results from complex analysis are assumed
 Language
 eng
 Extent
 1 online resource (xvii, 412 pages).
 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: HermiteBiehler Functions
 5. Generalized HermiteBiehler Functions
 6. Applications of Shifted HermiteBiehler 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 SturmLiouville Problems
 Bibliography
 Index
 Index of Notation
 Isbn
 9783319170695
 Label
 Spectral theory of operator pencils, HermiteBiehler functions, and their applications
 Title
 Spectral theory of operator pencils, HermiteBiehler functions, and their applications
 Statement of responsibility
 Manfred Möller, Vyacheslav Pivovarchik
 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 AnI for an operator A, and selfadjoint operators are of particular interest and importance, both theoretically and in terms of applications. A characteristic feature of selfadjoint 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 selfadjoint 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 HermiteBiehler 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 wellknown results from complex analysis are assumed
 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, HermiteBiehler functions, and their applications, Manfred Möller, Vyacheslav Pivovarchik
 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: HermiteBiehler Functions  5. Generalized HermiteBiehler Functions  6. Applications of Shifted HermiteBiehler 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 SturmLiouville 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
 10.1007/9783319170701
 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, HermiteBiehler functions, and their applications, Manfred Möller, Vyacheslav Pivovarchik
 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: HermiteBiehler Functions  5. Generalized HermiteBiehler Functions  6. Applications of Shifted HermiteBiehler 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 SturmLiouville 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
 10.1007/9783319170701
 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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History of Science CollectionsBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

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