Difference equations with a point interaction

Bayram E., Cebesoy Ş., Erdal İ.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.42, no.16, pp.5498-5508, 2019 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 16
  • Publication Date: 2019
  • Doi Number: 10.1002/mma.5449
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5498-5508
  • Keywords: asymptotic, difference equations, eigenvalues, impulsive conditions, spectral singularities, spectrum, SPECTRAL-ANALYSIS, 2ND-ORDER, OPERATORS
  • Ankara University Affiliated: Yes

Abstract

In this paper, we consider an impulsive second-order difference equation on the whole axis. We determine eigenvalues, spectral singularities, continuous spectrum corresponding to this difference equation with an impulsive condition by using the asymptotic properties of Jost functions, and uniqueness theorems of analytic functions. Finally, we demonstrate that the impulsive difference equation has finite number of eigenvalues and spectral singularities with finite multiplicities under certain conditions.