Quadraticeigenparameter-dependent quantum difference equations

Authors: YELDA AYGAR KÜÇÜKEVCİLİOĞLU

Abstract: 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.

Keywords: $q$-difference equation, Jost solution, spectral analysis, eigenvalue, spectral singularity

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