Principal functions of discrete Sturm-Liouville equations with hyperbolic eigenparameter

Yokus, Nihal and Coskun, Nimet

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creative_2017_26_3_353_359

DOI: https://doi.org/10.37193/CMI.2017.03.13

Issue no: Vol 26/2017 no. 3 Tags: spectral analysis, spectral singularities, eigenvalues, discrete equations

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In this study, we take under investigation principal functions corresponding to the eigenvalues and the spectral singularities of the boundary value problem (BVP) $a_{n-1}y_{n-1}+b_{n}y_{n}+a_{n}y_{n+1}=\lambda y_{n},$ $n\in \mathbb{N}$ and $\left( \gamma _{0}+\gamma _{1}\lambda \right) y_{1}+\left( \beta_{0}+\beta _{1}\lambda \right) y_{0}=0$ where $\left( a_{n}\right)$ and $\left( b_{n}\right)$ are complex sequences, $\lambda$ is a hyperbolic eigenparameter and $\gamma _{i},\beta _{i}\in \mathbb{C}$ for $i=0,1.$