LEADER 04948nam 22006735 450 001 9910299782503321 005 20200705162140.0 010 $a3-319-17070-8 024 7 $a10.1007/978-3-319-17070-1 035 $a(CKB)3710000000434100 035 $a(EBL)2096195 035 $a(SSID)ssj0001525113 035 $a(PQKBManifestationID)11887759 035 $a(PQKBTitleCode)TC0001525113 035 $a(PQKBWorkID)11485562 035 $a(PQKB)11092455 035 $a(DE-He213)978-3-319-17070-1 035 $a(MiAaPQ)EBC2096195 035 $a(PPN)186399936 035 $a(EXLCZ)993710000000434100 100 $a20150611d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSpectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications /$fby Manfred Möller, Vyacheslav Pivovarchik 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2015. 215 $a1 online resource (418 p.) 225 1 $aOperator Theory: Advances and Applications,$x0255-0156 ;$v246 300 $aDescription based upon print version of record. 311 $a3-319-17069-4 320 $aIncludes bibliographical references and indexes. 327 $aPreface -- 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. 330 $aThe theoretical part of this monograph examines the distribution of the spectrum of operator polynomials, focusing on quadratic operator polynomials with discrete spectra. The second part is devoted to applications. Standard spectral problems in Hilbert spaces are of the form A-?I for an operator A, and self-adjoint operators are of particular interest and importance, both theoretically and in terms of applications. A characteristic feature of self-adjoint operators is that their spectra are real, and many spectral problems in theoretical physics and engineering can be described by using them. However, a large class of problems, in particular vibration problems with boundary conditions depending on the spectral parameter, are represented by operator polynomials that are quadratic in the eigenvalue parameter and whose coefficients are self-adjoint operators. The spectra of such operator polynomials are in general no more real, but still exhibit certain patterns. The distribution of these spectra is the main focus of the present volume. For some classes of quadratic operator polynomials, inverse problems are also considered. The connection between the spectra of such quadratic operator polynomials and generalized Hermite-Biehler functions is discussed in detail. Many applications are thoroughly investigated, such as the Regge problem and damped vibrations of smooth strings, Stieltjes strings, beams, star graphs of strings and quantum graphs. Some chapters summarize advanced background material, which is supplemented with detailed proofs. With regard to the reader?s background knowledge, only the basic properties of operators in Hilbert spaces and well-known results from complex analysis are assumed. 410 0$aOperator Theory: Advances and Applications,$x0255-0156 ;$v246 606 $aOperator theory 606 $aDifferential equations 606 $aMathematical physics 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 615 0$aOperator theory. 615 0$aDifferential equations. 615 0$aMathematical physics. 615 14$aOperator Theory. 615 24$aOrdinary Differential Equations. 615 24$aMathematical Physics. 676 $a515.7222 700 $aMöller$b Manfred$4aut$4http://id.loc.gov/vocabulary/relators/aut$0149791 702 $aPivovarchik$b Vyacheslav$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299782503321 996 $aSpectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications$92540392 997 $aUNINA