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[null,"1.","Record Nr.",null,"UNISA996499867103316"]
[null,null,"Autore",null,"Carey Alan L."]
[null,null,"Titolo",null,"Index theory beyond the Fredholm case / / Alan L. Carey, Galina Levitina"]
[null,null,"Pubbl/distr/stampa",null,"Cham, Switzerland : , : Springer, , [2022]"]
[{"$nulls":4},"©2022"]
[null,null,"ISBN",null,"3-031-19436-5"]
[null,null,"Descrizione fisica",null,"1 online resource (186 pages)"]
[null,null,"Collana",null,"Lecture notes in mathematics ; ; Volume 2323"]
[null,null,"Disciplina",null,"512.556"]
[null,null,"Soggetti",null,"Index theory (Mathematics)"]
[{"$nulls":4},"Teoria de l'índex (Matemàtica)"]
[{"$nulls":4},"Llibres electrònics"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references."]
[null,null,"Nota di contenuto",null,"Intro -- Preface -- Acknowledgements -- Notations -- Contents -- 1 Introduction -- 1.1 Motivation and Background -- 1.2 An Overview of Recent Results -- 1.3 Discussion of the Methods and the Applications in These Notes -- 1.4 Summary of the Exposition -- 2 Double Operator Integrals -- 2.1 Double Operator Integrals in the Discrete Setting -- 2.2 Double Operator Integrals in the General Setting -- 2.3 Double Operator Integrals for Resolvent Comparable Operators -- 2.4 Continuity of Double Operator Integrals with Respect to the Operator Parameters -- 3 The Model Operator and Its Approximants -- 3.1 The Class of p-Relative Trace-Class Perturbations -- 3.2 Main Setting and Assumptions -- 4 The Spectral Shift Function -- 4.1 An Introduction to the Theory of the Spectral Shift Function -- 4.1.1 Perturbation Determinants -- 4.1.2 M. G. Krein' s Construction of the Spectral Shift Function -- 4.1.3 Properties of the Spectral Shift Function -- 4.2 More General Classes of Perturbations -- 4.2.1 Spectral Shift Function for Unitary Operators -- 4.2.2 Spectral Shift Function for Resolvent Comparable Operators -- 4.2.3 Invariance Principle -- 4.2.4 Spectral Shift Function for m-Resolvent Comparable Operators -- 4.3 Continuity of the Spectral Shift Function with Respect to the Operator Parameter -- 4.4 Representation of the Spectral Shift Function via a Regularised Perturbation Determinant -- 4.5 Spectral Shift Functions for the Pairs (A+,A-), (H2,H1) -- 5 Spectral Flow -- 5.1 Phillips' Definition of Spectral Flow and Analytic Formulas -- 5.1.1 The Variation of eta "]
[{"$nulls":4},"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."]
[{"$nulls":4},"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."]