Difference equations with a point interaction. (17th January 2019)

• Record Type: Journal Article
• Authors: Bairamov, Elgiz; Cebesoy, Serifenur; Erdal, Ibrahim
• Other Names: Yıldırım Kenan guestEditor.; Rasa Ioan guestEditor.; Acar Tuncer guestEditor.; Abazari Reza guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 16(2019)
• Page Start: 5498
• Page End: 5508
• Publication Date: 2019-01-17
• Subjects: asymptotic -- difference equations -- eigenvalues -- impulsive conditions -- spectral singularities -- spectrum; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5449
• Languages: English
• ISSNs: 0170-4214

Abstract

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.