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The spectrum of non-local discrete Schrödinger operators with a δ-potential

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journal contribution
posted on 27.05.2016, 13:22 by Fumio Hiroshima, Jozsef Lorinczi
The behaviour of the spectral edges (embedded eigenvalues and resonances) is discussed at the two ends of the continuous spectrum of non-local discrete Schrödinger operators with a δ-potential. These operators arise by replacing the discrete Laplacian by a strictly increasing C1-function of the discrete Laplacian. The dependence of the results on this function and the lattice dimension are explicitly derived. It is found that while in the case of the discrete Schrödinger operator these behaviours are the same no matter which end of the continuous spectrum is considered, an asymmetry occurs for the non-local cases. A classification with respect to the spectral edge behaviour is also offered.

Funding

FH is financially supported by Grant-in-Aid for Science Research (B) 23340032 from JSPS. JL thanks Institut Mittag-Leffler, Stockholm, for the opportunity to organise the research-in-peace workshop “Lieb-Thirring-type bounds for a class of Feller processes perturbed by a potential" during the period 25 July – 9 August 2013.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Pacific Journal of Mathematics for Industry

Volume

6

Issue

1

Citation

HIROSHIMA, F. and LORINCZI, J., 2014. The spectrum of non-local discrete Schrödinger operators with a δ-potential. Pacific Journal of Mathematics for Industry, 6 (7), doi: doi:10.1186/s40736-014-0007-8

Publisher

© Hiroshima and Lorinczi; licensee Springer.

Version

VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/ by/4.0/

Publication date

2014

Notes

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

eISSN

2198-4115

Language

en