Principal Functions of Non‐Selfadjoint Difference Operator with Spectral Parameter in Boundary Conditions

Abstract

We investigate the principal functions corresponding to the eigenvalues and the spectral singularities of the boundary value problem (BVP) , and , where and are complex sequences, is an eigenparameter, and , for , 1.

Spectrum and symmetries of the impulsive difference equations

“…Besides, impulsive di¤erence equations are basic tools to do investigations in numerical analysis having applications in economics, social sciences, biology, engineering, etc... For the mathematical theory of impulsive di¤erence equations, we refer to [6][7][8]. The spectral analysis of self-adjoint (Hermitian) and non-selfadjoint (non-Hermitian) di¤erence operators were investigated in detail by several authors [9][10][11][12]. But the theory of impulsive SPECTRUM AND SYM M ETRIES OF THE IM PULSIVE DIFFERENCE EQ UATIONS 39 di¤erence equations is a new and important branch of operator theory which is interesting and useful.…”

Principal functions of impulsive difference operators on semi axis

“…On the other hand, for di¤erence equations, a lot of spectral results have been investigated in the literature [12,13]. Moreover, for the spectral theory of di¤erence equations, [14,15,16,17,18,19,20] are detailed references for the readers. But these references are all related to general boundary conditions.…”

Quadraticeigenparameter-dependent quantum difference equations

“…Furthermore, quantum calculus received a lot of attention, and most of the published work has been interested in some problems of q -difference equations (see [2,6,3,11,10]). The spectral analysis of eigenparameter-dependent nonselfadjoint difference equations and q -difference equation were studied in [7,15,6,13]. A BVP for the discrete Sturm-Liouville equation consisting of second-order difference equation and boundary conditions that depend on a quadratic eigenvalue parameter was first studied by Koprubasi et al [13].…”