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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
The Limiting Absorption Principle for Massless Dirac Operators, Properties of Spectral Shift Functions, and an Application to the Witten Index of Non-Fredholm Operators cover
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Front matterDownload pp. i–iv
AbstractDownload pp. v–vi
ContentsDownload pp. vii–viii
1IntroductionDownload pp. 1–13
2Some background on (locally) smooth operatorsDownload pp. 15–21
3A limiting absorption principle for interacting, massless Dirac operatorsDownload pp. 23–35
4On the absence of eigenvalues for interacting, massless Dirac operatorsDownload pp. 37–39
5The Green’s functions of H0(m)H_0(m) and H0H_0Download pp. 41–47
6Trace ideal properties of F1( ⋅ )(H0−zI[L2(Rn)]N)−1F2( ⋅ )F_1(\,\cdot\,)(H_0 - z I_{[L^2(\mathbb{R}^n)]^N})^{-1} F_2(\,\cdot\,) and ⟨ ⋅ ⟩−δ(H0−zI[L2(Rn)]N)−1⟨ ⋅ ⟩−δ\langle\,\cdot\,\rangle^{-\delta}(H_0 - z I_{[L^2(\mathbb{R}^n)]^N})^{-1}\langle\,\cdot\,\rangle^{-\delta}Download pp. 49–61
7Powers of resolvents and trace idealsDownload pp. 63–67
8The spectral shift function: Abstract factsDownload pp. 69–79
9Representing ξ( ⋅ ;S,S0)\xi(\,\cdot\,;S,S_0) in terms of regularized Fredholm determinantsDownload pp. 81–89
10Analysis of Im⁡(FH,H0(λ+i0))\operatorname{Im}(F_{H,H_0}(\lambda + i0))Download pp. 91–117
11Analysis of GH;H0G_{H;H_0}Download pp. 119–143
12Analysis of ξ( ⋅ ;H,H0)\xi(\,\cdot\,;H,H_0) and an application to theWitten index for a class of non-Fredholm operatorsDownload pp. 145–156
ASome remarks on block matrix operatorsDownload pp. 157–161
BAsymptotic results for Hankel functionsDownload pp. 163–174
CExpansions and estimates of the free Dirac Green’s matrixDownload pp. 175–189
DA product formula for modified Fredholm determinantsDownload pp. 191–198
ENotational conventionsDownload pp. 199–202
ReferencesDownload pp. 203–213