01251cam0 2200289 450 E60020006559220211103090845.020100713d1968 |||||ita|0103 bagerBEÜber die verschiednen Methoden des Philosophirens und die verschiednen Systeme der Philosophie in Rücksicht ihrer allgemeinen Gültigkeit. Eine Beylage zum Organonvon Wilhelm Traugott KrugImpression anastaltiqueBruxellesCulture et Civilisation1968XIII, 53 p.19 cmAetas kantiana159Ripr. facs. dell'ed. : Meissen, 1802001LAEC000284802001 *Aetas kantiana159Krug, Wilhelm TraugottA600200061864070220514ITUNISOB20211103RICAUNISOBUNISOB100|Coll|19|k18468E600200065592M 102 Monografia moderna SBNM100|Coll|19|k000159Si18468acquistocutoloUNISOBUNISOB20100713131444.020211103090831.0AlfanoÜber die verschiednen Methoden des Philosophirens und die verschiednen Systeme der Philosophie in Rücksicht ihrer allgemeinen Gültigkeit569166UNISOB04421nam 2200505 450 99649986710331620230512095424.03-031-19436-5(MiAaPQ)EBC7150620(Au-PeEL)EBL7150620(CKB)25510405700041(OCoLC)1352972743(PPN)26634822X(EXLCZ)992551040570004120230416d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierIndex theory beyond the Fredholm case /Alan L. Carey, Galina LevitinaCham, Switzerland :Springer,[2022]©20221 online resource (186 pages)Lecture notes in mathematics ;Volume 2323Print version: Carey, Alan Index Theory Beyond the Fredholm Case Cham : Springer,c2023 9783031194351 Includes bibliographical references.Intro -- 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.6.2 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 (Dα+φ, Dα) -- 7.2.3 The Index of the Operator DA -- 7.2.4 Spectral Flow Along the path {Dα+θ(t)φ}tR -- 7.2.5 The Anomaly for the Operator DA -- References.Lecture notes in mathematics (Springer-Verlag) ;Volume 2323.Index theory (Mathematics)Teoria de l'índex (Matemàtica)thubLlibres electrònicsthubIndex theory (Mathematics)Teoria de l'índex (Matemàtica)512.556Carey Alan L.61721Levitina GalinaMiAaPQMiAaPQMiAaPQBOOK996499867103316Index theory beyond the Fredholm case3088867UNISA