The Effects of Hyperbolic Eigenparameter on Spectral Analysis of a Quantum Difference Equations

AYGAR KÜÇÜKEVCİLİOĞLU Y.

MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES, vol.11, no.3, pp.317-330, 2017 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 3
  • Publication Date: 2017
  • Journal Name: MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.317-330
  • Keywords: Eigenvalue, spectral singularity, q-difference equation, green function, Jost solution, resolvent
  • Ankara University Affiliated: Yes

Abstract

In this study, second-order nonselfadjoint expression and its associated boundary condition depending on an hyperbolic eigenparameter are discussed. We introduce the sets of eigenvalues and spectral singularities of a boundary value problem (BVP) which is defined with same quantum difference expression and boundary condition. Next, some spectral properties of eigenvalues and spectral singularities are investigated using the Jost solution, green function and resolvent operator of this BVP.