Buch, Englisch, Band 2323, 175 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 300 g
Reihe: Lecture Notes in Mathematics
Buch, Englisch, Band 2323, 175 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 300 g
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-031-19435-1
Verlag: Springer Nature Switzerland
Creating a coherent picture of numerous investigations and scattered notions of the past 50 years, this work carefully introduces spectral flow, the Witten index and the spectral shift function and describes their relationship. After the introduction, Chapter 2 carefully reviews Double Operator Integrals, Chapter 3 describes the class of so-called p-relative trace class perturbations, followed by the construction of Krein's spectral shift function in Chapter 4. Chapter 5 reviews the analytic approach to spectral flow, culminating in Chapter 6 in the main abstract result of the book, namely the so-called principal trace formula. Chapter 7 completes the work with illustrations of the main results using explicit computations on two examples: the Dirac operator in Rd, and a differential operator on an interval. Throughout, attention is paid to the history of the subject and earlier references are provided accordingly. The book is aimed at experts in index theory as well as newcomers to the field.
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Weitere Infos & Material
- 1. Introduction. - 2. Double Operator Integrals. - 3. The Model Operator and Its Approximants. - 4. The Spectral Shift Function. - 5. Spectral Flow. - 6. The Principal Trace Formula and Its Applications. - 7. Examples.