Abstract
In this paper, we study the spectral properties of a second order difference operator with a growing potential. The operator acts in the complex Hilbert space ℓ2(Z) of square summable complex sequences indexed by the integers. This operator is a discrete analogue of a second order differential operator with a growing complex potential. The study is based on a method of similar operators developed by A. G. Baskakov and his collaborators. This method allows us to reduce the study of the operator to one with a block-diagonal matrix. Asymptotic estimates of eigenvalues, eigenvectors, and spectral projections of a difference operator are obtained.
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.
