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

Abstract : This paper deals with the study of the two-dimensional Dirac operator with infinite mass boundary condition in a sector. 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 byproduct of this analysis we are able to give self-adjointness results on polygones. We also discuss the question of distinguished self-adjoint extensions and study basic spectral properties of the operator in the sector.
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Submitted on : Wednesday, July 11, 2018 - 10:16:05 AM
Last modification on : Sunday, June 26, 2022 - 12:08:54 PM
Long-term archiving on: : Monday, October 1, 2018 - 1:13:57 AM

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Loïc Le Treust, Thomas Ourmières-Bonafos. Self-Adjointness of Dirac Operators with Infinite Mass Boundary Conditions in Sectors. Annales Henri Poincaré, Springer Verlag, 2018, 19 (5), pp.1465 - 1487. ⟨10.1007/s00023-018-0661-y⟩. ⟨hal-01561490v2⟩

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