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  2. Regning og matematisk analyse
  3. Funktionsanalyse og transformation

Index Theory Beyond the Fredholm Case

Af: Alan Carey, Galina Levitina Engelsk Paperback

Index Theory Beyond the Fredholm Case

Af: Alan Carey, Galina Levitina Engelsk Paperback
Tjek vores konkurrenters priser
This book is about extending index theory to some examples where non-Fredholm operators arise. It focuses on one aspect of the problem of what replaces the notion of spectral flow and the Fredholm index when the operators in question have zero in their essential spectrum. Most work in this topic stems from the so-called Witten index that is discussed at length here. The new direction described in these notes is the introduction of `spectral flow beyond the Fredholm case''.

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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This book is about extending index theory to some examples where non-Fredholm operators arise. It focuses on one aspect of the problem of what replaces the notion of spectral flow and the Fredholm index when the operators in question have zero in their essential spectrum. Most work in this topic stems from the so-called Witten index that is discussed at length here. The new direction described in these notes is the introduction of `spectral flow beyond the Fredholm case''.

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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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 175
ISBN-13: 9783031194351
Indbinding: Paperback
Udgave:
ISBN-10: 3031194357
Kategori: Funktionsanalyse og transformation
Udg. Dato: 2 dec 2022
Længde: 14mm
Bredde: 234mm
Højde: 155mm
Forlag: Springer International Publishing AG
Oplagsdato: 2 dec 2022
Forfatter(e): Alan Carey, Galina Levitina
Forfatter(e) Alan Carey, Galina Levitina

Kategori Funktionsanalyse og transformation

ISBN-13 9783031194351

Sprog Engelsk

Indbinding Paperback

Sider 175

Udgave

Længde 14mm

Bredde 234mm

Højde 155mm

Udg. Dato 2 dec 2022

Oplagsdato 2 dec 2022

Forlag Springer International Publishing AG

Kategori sammenhænge