The main aim of this paper is to construct quantum extension of the discrete Sturm--Liouville equation consisting of second-order difference equation and boundary conditions that depend on a quadratic eigenvalue parameter. We consider a boundary value problem (BVP) consisting of a second-order quantum difference equation and boundary conditions that depend on the quadratic eigenvalue parameter. We present a condition that guarantees that this BVP has a finite number of eigenvalues and spectral singularities with finite multiplicities.
$q$-difference equation, Jost solution, spectral analysis, eigenvalue, spectral singularity
KÜÇÜKEVCİLİOĞLU, YELDA AYGAR
"Quadraticeigenparameter-dependent quantum difference equations,"
Turkish Journal of Mathematics: Vol. 40:
2, Article 19.
Available at: https://journals.tubitak.gov.tr/math/vol40/iss2/19