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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.
Cited literature [36 references]
https://hal.archives-ouvertes.fr/hal-01561490
Contributor : Loïc Le Treust Connect in order to contact the contributor
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
Contributor : Loïc Le Treust Connect in order to contact the contributor
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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