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Annales Henri Poincaré

, Volume 19, Issue 7, pp 1993–2019 | Cite as

On the Global Limiting Absorption Principle for Massless Dirac Operators

  • Alan Carey
  • Fritz Gesztesy
  • Jens Kaad
  • Galina Levitina
  • Roger Nichols
  • Denis Potapov
  • Fedor Sukochev
Article

Abstract

We prove a global limiting absorption principle on the entire real line for free, massless Dirac operators \(H_0 = \alpha \cdot (-i \nabla )\) for all space dimensions \(n \in {{\mathbb {N}}}\), \(n \geqslant 2\). This is a new result for all dimensions other than three, in particular, it applies to the two-dimensional case which is known to be of some relevance in applications to graphene. We also prove an essential self-adjointness result for first-order matrix-valued differential operators with Lipschitz coefficients.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Alan Carey
    • 1
    • 2
  • Fritz Gesztesy
    • 3
  • Jens Kaad
    • 4
  • Galina Levitina
    • 5
  • Roger Nichols
    • 6
  • Denis Potapov
    • 5
  • Fedor Sukochev
    • 5
  1. 1.Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia
  2. 2.School of Mathematics and Applied StatisticsUniversity of WollongongWollongongAustralia
  3. 3.Department of MathematicsBaylor UniversityWacoUSA
  4. 4.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdense MDenmark
  5. 5.School of Mathematics and StatisticsUNSWKensingtonAustralia
  6. 6.Mathematics DepartmentThe University of Tennessee at ChattanoogaChattanoogaUSA

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