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Annales Henri Poincaré

, Volume 19, Issue 5, pp 1465–1487 | Cite as

Self-Adjointness of Dirac Operators with Infinite Mass Boundary Conditions in Sectors

  • Loïc Le Treust
  • Thomas Ourmières-Bonafos
Article

Abstract

This paper deals with the study of the two-dimensional Dirac operator with infinite mass boundary conditions in sectors. We investigate the question of self-adjointness depending on the aperture of the sector: when the sector is convex it is self-adjoint on a usual Sobolev space, whereas when the sector is non-convex it has a family of self-adjoint extensions parametrized by a complex number of the unit circle. As a by-product of the analysis, we are able to give self-adjointness results on polygonal domains. We also discuss the question of distinguished self-adjoint extensions and study basic spectral properties of the Dirac operator with a mass term in the sector.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CNRS, Centrale Marseille, I2MAix Marseille UnivMarseilleFrance
  2. 2.Laboratoire Mathématiques d’OrsayUniv. Paris-SudOrsayFrance
  3. 3.CNRSUniversité Paris-SaclayParisFrance

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