LEADER 03952nam 22006975 450 001 9910483337603321 005 20251113200149.0 010 $a3-030-59088-7 024 7 $a10.1007/978-3-030-59088-8 035 $a(CKB)4100000011528502 035 $a(MiAaPQ)EBC6380792 035 $a(DE-He213)978-3-030-59088-8 035 $a(MiAaPQ)EBC6647514 035 $a(Au-PeEL)EBL6380792 035 $a(OCoLC)1225353737 035 $a(Au-PeEL)EBL6647514 035 $a(PPN)254975658 035 $a(EXLCZ)994100000011528502 100 $a20201027d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSpectral and Scattering Theory for Ordinary Differential Equations $eVol. I: Sturm?Liouville Equations /$fby Christer Bennewitz, Malcolm Brown, Rudi Weikard 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (IX, 379 p.) 225 1 $aUniversitext,$x2191-6675 311 08$a3-030-59087-9 320 $aIncludes bibliographical references and index. 327 $a1 Introduction -- 2 Hilbert space -- 3 Abstract spectral theory -- 4 Sturm?Liouville equations -- 5 Left-definite Sturm?Liouville equations -- 6 Oscillation, spectral asymptotics and special functions -- 7 Uniqueness of the inverse problem -- 8 Scattering -- A Functional analysis -- B Stieltjes integrals -- C Schwartz distributions -- D Ordinary differential equations -- E Analytic functions -- F The Camassa?Holm equation -- References -- Symbol Index -- Subject Index. 330 $aThis graduate textbook offers an introduction to the spectral theory of ordinary differential equations, focusing on Sturm?Liouville equations. Sturm?Liouville theory has applications in partial differential equations and mathematical physics. Examples include classical PDEs such as the heat and wave equations. Written by leading experts, this book provides a modern, systematic treatment of the theory. The main topics are the spectral theory and eigenfunction expansions for Sturm?Liouville equations, as well as scattering theory and inverse spectral theory. It is the first book offering a complete account of the left-definite theory for Sturm?Liouville equations. The modest prerequisites for this book are basic one-variable real analysis, linear algebra, as well as an introductory course in complex analysis. More advanced background required in some parts of the book is completely covered in the appendices. With exercises in each chapter, the book is suitable for advanced undergraduate and graduate courses, either as an introduction to spectral theory in Hilbert space, or to the spectral theory of ordinary differential equations. Advanced topics such as the left-definite theory and the Camassa?Holm equation, as well as bibliographical notes, make the book a valuable reference for experts. 410 0$aUniversitext,$x2191-6675 606 $aMathematical analysis 606 $aOperator theory 606 $aSpecial functions 606 $aMathematical physics 606 $aAnalysis 606 $aOperator Theory 606 $aSpecial Functions 606 $aMathematical Physics 615 0$aMathematical analysis. 615 0$aOperator theory. 615 0$aSpecial functions. 615 0$aMathematical physics. 615 14$aAnalysis. 615 24$aOperator Theory. 615 24$aSpecial Functions. 615 24$aMathematical Physics. 676 $a515.352 700 $aBennewitz$b Christer$f1943-$059796 702 $aWeikard$b Rudi$f1958- 702 $aBrown$b Malcolm 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483337603321 996 $aSpectral and Scattering Theory for Ordinary Differential Equations$91889267 997 $aUNINA