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
Fritz Gesztesy
Baylor University, Waco, USA
Galina Levitina
Australian National University, Canberra, Australia
Roger Nichols
The University of Tennessee at Chattanooga, USA
Fedor Sukochev
University of New South Wales, Sydney, Australia
Dmitriy Zanin
University of New South Wales, Sydney, Australia

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