The Limiting Absorption Principle for Massless Dirac Operators, Properties of Spectral Shift Functions, and an Application to the Witten Index of Non-Fredholm Operators

Alan Carey
Australian National University, Canberra; and University of Wollongong, Australia
- MathSciNet
- zbMATH Open
Fritz Gesztesy
Baylor University, Waco, USA
Galina Levitina
Australian National University, Canberra, Australia
Roger Nichols
The University of Tennessee at Chattanooga, USA
- MathSciNet
- zbMATH Open
Dmitriy Zanin
University of New South Wales, Sydney, Australia
- MathSciNet
- zbMATH Open
Fedor Sukochev
University of New South Wales, Sydney, Australia
- MathSciNet
- zbMATH Open

This book is published open access.

	Front matterDownload pp. i–iv
	AbstractDownload pp. v–vi
	ContentsDownload pp. vii–viii
1	IntroductionDownload pp. 1–13
2	Some background on (locally) smooth operatorsDownload pp. 15–21
3	A limiting absorption principle for interacting, massless Dirac operatorsDownload pp. 23–35
4	On the absence of eigenvalues for interacting, massless Dirac operatorsDownload pp. 37–39
5	The Green’s functions of $H_{0} (m)$ and $H_{0}$ Download pp. 41–47
6	Trace ideal properties of $F_{1} (\cdot) (H_{0} - z I_{[L^{2} (R^{n})]^{N}})^{- 1} F_{2} (\cdot)$ and $⟨ \cdot ⟩^{- δ} (H_{0} - z I_{[L^{2} (R^{n})]^{N}})^{- 1} ⟨ \cdot ⟩^{- δ}$ Download pp. 49–61
7	Powers of resolvents and trace idealsDownload pp. 63–67
8	The spectral shift function: Abstract factsDownload pp. 69–79
9	Representing $ξ (\cdot; S, S_{0})$ in terms of regularized Fredholm determinantsDownload pp. 81–89
10	Analysis of $Im (F_{H, H_{0}} (λ + i 0))$ Download pp. 91–117
11	Analysis of $G_{H; H_{0}}$ Download pp. 119–143
12	Analysis of $ξ (\cdot; H, H_{0})$ and an application to theWitten index for a class of non-Fredholm operatorsDownload pp. 145–156
A	Some remarks on block matrix operatorsDownload pp. 157–161
B	Asymptotic results for Hankel functionsDownload pp. 163–174
C	Expansions and estimates of the free Dirac Green’s matrixDownload pp. 175–189
D	A product formula for modified Fredholm determinantsDownload pp. 191–198
E	Notational conventionsDownload pp. 199–202
	ReferencesDownload pp. 203–213