LEADER 03869nam 2200697Ia 450 001 9910814895903321 005 20200520144314.0 010 $a1-282-82115-6 010 $a9786612821158 010 $a1-4008-3705-7 024 7 $a10.1515/9781400837052 035 $a(CKB)2670000000056325 035 $a(EBL)590814 035 $a(OCoLC)677162060 035 $a(SSID)ssj0000429275 035 $a(PQKBManifestationID)11965344 035 $a(PQKBTitleCode)TC0000429275 035 $a(PQKBWorkID)10430188 035 $a(PQKB)10485522 035 $a(WaSeSS)Ind00024857 035 $a(DE-B1597)446625 035 $a(OCoLC)979579169 035 $a(DE-B1597)9781400837052 035 $a(Au-PeEL)EBL590814 035 $a(CaPaEBR)ebr10421701 035 $a(CaONFJC)MIL282115 035 $a(PPN)199245010 035 $a(FR-PaCSA)88838078 035 $a(MiAaPQ)EBC590814 035 $a(EXLCZ)992670000000056325 100 $a20100621d2010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSzego?'s theorem and its descendants $espectral theory for L2 perturbations of orthogonal polynomials /$fBarry Simon 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$d2010 215 $a1 online resource (663 p.) 225 0 $aPorter Lectures ;$v6 300 $aDescription based upon print version of record. 311 $a0-691-14704-3 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tContents -- $tPreface -- $tChapter One. Gems of Spectral Theory -- $tChapter Two. Szeg?'s Theorem -- $tChapter Three The Killip-Simon Theorem: Szeg? for OPRL -- $tChapter Four. Sum Rules and Consequences for Matrix Orthogonal Polynomials -- $tChapter Five. Periodic OPRL -- $tChapter Six. Toda Flows and Symplectic Structures -- $tChapter Seven. Right Limits -- $tChapter Eight. Szeg? and Killip-Simon Theorems for Periodic OPRL -- $tChapter Nine. Szeg?'s Theorem for Finite Gap OPRL -- $tChapter Ten. A.C. Spectrum for Bethe-Cayley Trees -- $tBibliography -- $tAuthor Index -- $tSubject Index 330 $aThis book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC. 410 0$aPorter Lectures 606 $aSpectral theory (Mathematics) 606 $aOrthogonal polynomials 615 0$aSpectral theory (Mathematics) 615 0$aOrthogonal polynomials. 676 $a515/.55 686 $aSK 680$2rvk 700 $aSimon$b Barry$f1946-$041965 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910814895903321 996 $aSzego?'s theorem and its descendants$93914906 997 $aUNINA