LEADER 01435nam0-2200409---450- 001 990000820880203316 005 20060705124902.0 035 $a0082088 035 $aUSA010082088 035 $a(ALEPH)000082088USA01 035 $a0082088 100 $a20011220d1974----km-y0ITAy01------ba 101 $aita 102 $aIT 105 $a||||||||001yy 200 1 $a<> tipografia napoletana nel '500$eannali di Giuseppe Cacchi, Giovanni Battista Cappelli e tipografi minori (1566-1600)$fPietro Manzi 210 $aFirenze$cOlschki$d1974 215 $a263 p$c24 tav.$d25 cm 225 2 $aBiblioteca di bibliografia italiana$x0067-7418 410 $12001$aBiblioteca di bibliografia italiana$x0067-7418 606 0 $aTipografia$yNapoli$xStoria$z16. 606 0 $aCacchi, Giuseppe$xAnnali tipografici$z1566-1593 606 0 $aCappelli, Giovanni Battista$xAnnali tipografici$z1572-1601 676 $a686.20945731 700 1$aMANZI,$bPietro$0201624 801 0$aIT$bsalbc$gISBD 912 $a990000820880203316 951 $aI.2. Coll.4/ 9/5(XIII COLL 3/77)$b129100 L.M.$cXIII COLL 959 $aBK 969 $aUMA 979 $aPATTY$b90$c20011220$lUSA01$h1709 979 $c20020403$lUSA01$h1728 979 $aPATRY$b90$c20040406$lUSA01$h1656 979 $aCOPAT2$b90$c20050224$lUSA01$h1511 979 $aCAPRIOLO$b90$c20060705$lUSA01$h1249 996 $aTipografia napoletana nel '500$9144262 997 $aUNISA LEADER 02044nam2 2200373 i 450 001 SUN0056313 005 20200302111412.248 010 $a978-35-401-3829-7$d0.00 100 $a20061117d1994 |0engc50 ba 101 $aeng 102 $aDE 105 $a|||| ||||| 200 1 $a4: *Fourier integral operators$fLars Hörmander 210 $aBerlin$cSpringer$d1994 215 $aVII, 351 p.$d24 cm. 410 1$1001SUN0024107$12001 $a*Grundlehren der mathematischen Wissenschaften$eA series of comprehensive texts in mathematics$v275$1210 $aBerlin$cSpringer$d1921-. 461 1$1001SUN0056311$12001 $aThe *analysis of linear partial differential operators$fLars Hörmander$v4$1210 $aBerlin$cSpringer$1215 $av.$d24 cm. 606 $a35-XX$xPartial differential equations [MSC 2020]$2MF$3SUNC019763 606 $a35S05$xPseudodifferential operators as generalizations of partial differential operators [MSC 2020]$2MF$3SUNC019841 606 $a58J50$xSpectral problems; spectral geometry; scattering theory on manifolds [MSC 2020]$2MF$3SUNC021225 606 $a47Fxx$xPartial differential operators [MSC 2020]$2MF$3SUNC022222 606 $a35P25$xScattering theory for PDEs [MSC 2020]$2MF$3SUNC022714 606 $a58J40$xPseudodifferential and Fourier integral operators on manifolds [MSC 2020]$2MF$3SUNC022823 606 $a58J32$xBoundary value problems on manifolds [MSC 2020]$2MF$3SUNC022824 606 $a58J47$xPropagation of singularities; initial value problems on manifolds [MSC 2020]$2MF$3SUNC022827 606 $a47G30$xPseudodifferential operators [MSC 2020]$2MF$3SUNC029207 620 $dBerlin$3SUNL000066 700 1$aHörmander$b, Lars$3SUNV046028$031879 712 $aSpringer$3SUNV000178$4650 801 $aIT$bSOL$c20201026$gRICA 912 $aSUN0056313 950 $aUFFICIO DI BIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$d08PREST 35-XX 1945 $e08 2529 IV 20061117 996 $aFourier integral operators$9957945 997 $aUNICAMPANIA LEADER 04421nam 2200505 450 001 996499867103316 005 20230512095424.0 010 $a3-031-19436-5 035 $a(MiAaPQ)EBC7150620 035 $a(Au-PeEL)EBL7150620 035 $a(CKB)25510405700041 035 $a(OCoLC)1352972743 035 $a(PPN)26634822X 035 $a(EXLCZ)9925510405700041 100 $a20230416d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIndex theory beyond the Fredholm case /$fAlan L. Carey, Galina Levitina 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (186 pages) 225 1 $aLecture notes in mathematics ;$vVolume 2323 311 08$aPrint version: Carey, Alan Index Theory Beyond the Fredholm Case Cham : Springer,c2023 9783031194351 320 $aIncludes bibliographical references. 327 $aIntro -- Preface -- Acknowledgements -- Notations -- Contents -- 1 Introduction -- 1.1 Motivation and Background -- 1.2 An Overview of Recent Results -- 1.3 Discussion of the Methods and the Applications in These Notes -- 1.4 Summary of the Exposition -- 2 Double Operator Integrals -- 2.1 Double Operator Integrals in the Discrete Setting -- 2.2 Double Operator Integrals in the General Setting -- 2.3 Double Operator Integrals for Resolvent Comparable Operators -- 2.4 Continuity of Double Operator Integrals with Respect to the Operator Parameters -- 3 The Model Operator and Its Approximants -- 3.1 The Class of p-Relative Trace-Class Perturbations -- 3.2 Main Setting and Assumptions -- 4 The Spectral Shift Function -- 4.1 An Introduction to the Theory of the Spectral Shift Function -- 4.1.1 Perturbation Determinants -- 4.1.2 M. G. Krein' s Construction of the Spectral Shift Function -- 4.1.3 Properties of the Spectral Shift Function -- 4.2 More General Classes of Perturbations -- 4.2.1 Spectral Shift Function for Unitary Operators -- 4.2.2 Spectral Shift Function for Resolvent Comparable Operators -- 4.2.3 Invariance Principle -- 4.2.4 Spectral Shift Function for m-Resolvent Comparable Operators -- 4.3 Continuity of the Spectral Shift Function with Respect to the Operator Parameter -- 4.4 Representation of the Spectral Shift Function via a Regularised Perturbation Determinant -- 4.5 Spectral Shift Functions for the Pairs (A+,A-), (H2,H1) -- 5 Spectral Flow -- 5.1 Phillips' Definition of Spectral Flow and Analytic Formulas -- 5.1.1 The Variation of eta Formula -- 5.1.2 A Review of Analytic Formulas for Spectral Flow -- 5.2 The Relation Between the Spectral Shift Function and the Spectral Flow -- 5.3 Generalised Spectral Flow -- 6 The Principal Trace Formula and Its Applications -- 6.1 A Brief History of the Principal Trace Formula. 327 $a6.2 Proving the Principal Trace Formula -- 6.3 A Generalised Pushnitski Formula -- 6.4 The Witten Index -- 6.4.1 Preliminaries -- 6.4.2 The Formula in Terms of the Spectral Shift Function -- 6.5 Cyclic Homology and Invariance -- 6.5.1 How the Witten Index Relates to This -- 6.5.2 Higher Schatten Classes -- 6.6 The Anomaly in Terms of the Spectral Shift Function -- 6.6.1 The Origin of the Notion of an `Anomaly' -- 6.6.2 Relationship to the Spectral Shift Function -- 7 Examples -- 7.1 The Dirac Operator in Rd -- 7.1.1 The Setting -- 7.1.2 Verification of Hypothesis 3.2.5 -- 7.1.3 The Index of DA -- 7.1.4 Behaviour of the Spectral Shift Function for the Massless Dirac Operator -- 7.2 A Compact One-Dimensional Example -- 7.2.1 The Setting -- 7.2.2 Spectral Shift Function of the Pair (D?+?, D?) -- 7.2.3 The Index of the Operator DA -- 7.2.4 Spectral Flow Along the path {D?+?(t)?}tR -- 7.2.5 The Anomaly for the Operator DA -- References. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$vVolume 2323. 606 $aIndex theory (Mathematics) 606 $aTeoria de l'índex (Matemàtica)$2thub 608 $aLlibres electrònics$2thub 615 0$aIndex theory (Mathematics) 615 7$aTeoria de l'índex (Matemàtica) 676 $a512.556 700 $aCarey$b Alan L.$061721 702 $aLevitina$b Galina 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996499867103316 996 $aIndex theory beyond the Fredholm case$93088867 997 $aUNISA