Abstract
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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
