Title

A Polynomial-Type Jost Solution and Spectral Properties of a Self-Adjoint Quantum-Difference Operator

Abstract

In this paper, we find a polynomial-type Jost solution of a self-adjoint q-difference equation of second order. Then we investigate the analytical properties and asymptotic behavior of the Jost solution. We prove that the self-adjoint operator L generated by the q-difference expression of second order has essential spectrum filling the segment [-2√q,2√q], q > 1. Finally, we examine the properties of the eigenvalues of L.

Department(s)

Mathematics and Statistics

International Standard Serial Number (ISSN)

1661-8254; 1661-8262

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2016 Birkhäuser Verlag, All rights reserved.

Publication Date

01 Aug 2016

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