dc.contributor.author Mas A. en_US dc.contributor.author Pizzichillo F. en_US dc.date.accessioned 2017-08-03T15:51:55Z dc.date.available 2017-08-03T15:51:55Z dc.date.issued 2017-08-03 dc.identifier.issn 0022-2488 dc.identifier.uri http://hdl.handle.net/20.500.11824/714 dc.description.abstract This note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$-shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by finding sharp constants and minimizers of some precise inequalities related to an uncertainty principle. On the other hand, we prove that the domains given by Dittrich, Exner and Seba en_US [Dirac operators with a spherically symmetric $\delta$-shell interaction, J. Math. Phys. 30.12 (1989), 2875-2882] and by Arrizabalaga, Mas and Vega [Shell interactions for Dirac operators, J. Math. Pures et Appl. 102.4 (2014), 617-639] for the realization of an electrostatic spherical shell interaction coincide. Finally, we explore the spectral relation between the shell interaction and its approximation by short range potentials with shrinking support, improving previous results in the spherical case. dc.format application/pdf en_US dc.language.iso eng en_US dc.publisher Journal of Mathematical Physics en_US dc.relation info:eu-repo/grantAgreement/EC/H2020/669689 en_US dc.relation ES/1PE/SEV-2013-0323 en_US dc.relation ES/1PE/MTM2014-53145-P en_US dc.relation EUS/BERC/BERC.2014-2017 en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Dirac operator, self-adjoint extension, spherical $\delta$-shell interaction, singular integral, approximation by scaled regular potentials en_US dc.title The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation en_US dc.type info:eu-repo/semantics/article en_US dc.type info:eu-repo/semantics/acceptedVersion en_US dc.identifier.doi 10.1063/1.5000381
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