@article{10902/29138,
year = {2017},
month = {8},
url = {https://hdl.handle.net/10902/29138},
abstract = {This note revolves on the free Dirac operator in R3 and its δ-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 et al. [J. Math. Phys. 30(12), 2875-2882 (1989)] and by Arrizabalaga et al. [J. Math. Pures Appl. 102(4), 617-639 (2014)] 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.},
organization = {We would like to thank Aingeru Fernández-Bertolín for addressing us Ref. 4 and for the enlightening discussions. Mas was supported by the Juan de la Cierva Program No. JCI2012-14073 and the funding Project Nos. MTM2011-27739 and MTM2014-52402 from the Government of Spain. Pizzichillo was supported by the MINECO Project No. MTM2014-53145-P, by the Basque Government through the BERC 2014-2017 program and by the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa accreditation SEV-2013-0323. Both authors were also supported by the ERCEA, Advanced Grant Project No. 669689 HADE.},
publisher = {American Institute of Physics},
publisher = {Journal of Mathematical Physics, 2017, 58(8), 082102},
title = {The relativistic spherical δ-shell interaction in R3: Spectrum and approximation},
author = {Mas Blesa, Albert and Pizzichillo, Fabio},
}