The spectrum of non-local discrete Schrödinger operators with a δ-potential
journal contributionposted 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.
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.
- Mathematical Sciences