ECM - Ecole Centrale de Marseille : UMR7373 (Pôle de l'étoile
Technopole de Château-Gombert
38 rue Frédéric Joliot-Curie
13013 Marseille, France - France)
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.
https://hal.archives-ouvertes.fr/hal-01561490
Contributeur : Loïc Le Treust
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Soumis le : mercredi 11 juillet 2018 - 10:16:05
Dernière modification le : jeudi 12 juillet 2018 - 01:31:53
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〉
