04975nam 22006735 450 991029978250332120200705162140.03-319-17070-810.1007/978-3-319-17070-1(CKB)3710000000434100(EBL)2096195(SSID)ssj0001525113(PQKBManifestationID)11887759(PQKBTitleCode)TC0001525113(PQKBWorkID)11485562(PQKB)11092455(DE-He213)978-3-319-17070-1(MiAaPQ)EBC2096195(PPN)186399936(EXLCZ)99371000000043410020150611d2015 u| 0engur|n|---|||||txtccrSpectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications[electronic resource] /by Manfred Möller, Vyacheslav Pivovarchik1st ed. 2015.Cham :Springer International Publishing :Imprint: Birkhäuser,2015.1 online resource (418 p.)Operator Theory: Advances and Applications,0255-0156 ;246Description based upon print version of record.3-319-17069-4 Includes bibliographical references and indexes.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.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.Operator Theory: Advances and Applications,0255-0156 ;246Operator theoryDifferential equationsMathematical physicsOperator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Ordinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Mathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Operator theory.Differential equations.Mathematical physics.Operator Theory.Ordinary Differential Equations.Mathematical Physics.515.7222Möller Manfredauthttp://id.loc.gov/vocabulary/relators/aut149791Pivovarchik Vyacheslavauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299782503321Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications2540392UNINA