Maqola

Bound states of Schrödinger-type operators on one and two dimensional lattices

Shokhrukh Yu. KholmatovUniversity of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, AustriaS. N. LakaevSamarkand State University, University boulevard 15, 140104 Samarkand, UzbekistanFirdavsjon M. AlmuratovSamarkand State University, University boulevard 15, 140104 Samarkand, Uzbekistan

Journal of Mathematical Analysis and Applicationsjournal2021en

ABI

Annotatsiya

We study the spectral properties of the Schrödinger-type operatorHˆμ:=Hˆ0+μVˆ,μ≥0, associated to a one-particle system in d-dimensional lattice Zd, d=1,2, where the non-perturbed operator Hˆ0 is a self-adjoint convolution-type operator generated by a Hopping matrix eˆ:Zd→C and the potential Vˆ is the multiplication operator by vˆ:Zd→R. Under certain regularity assumption on eˆ and a decay assumption on vˆ, we establish the existence or non-existence and also the finiteness of eigenvalues of Hˆμ. Moreover, in the case of existence we study the asymptotics of eigenvalues of Hˆμ as μ↘0.

Mavzular

Spectral Theory in Mathematical Physics Matrix Theory and Algorithms Mathematical Approximation and Integration

Identifikatorlar

DOI: 10.1016/j.jmaa.2021.125280

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