Spectral Analysis of Klein-Gordon dierence operator given by a general boundary condition

Nihal Yokus, Nimet Coskun

Abstract


In this study, we consider the spectral properties of the non-selfadjoint difference operator \(L\) generated in \(l_2(\mathbb{N})\) by the difference expression $$ \Delta (a_{n-1}\Delta y_{n-1})+(v_n-\lambda)^2y_n=0, \ \ n \in \mathbb{N},$$ and a general boundary condition $$\sum^\infty_{n=0} h_ny_n=0,$$ where \(a_0 = 1\), \(h_0\neq 0\) and \(\{a_n\}^\infty_{n=1}\), \(\{v_n\}^\infty_{n=1}\) and \(\{h_n\}^\infty_{n=1}\) are complex sequences and \(\{h_n\}^\infty_{n=1}\in l_1(\mathbb{N})\). Along with the designation of the sets of eigenvalues and spectral singularities of the operator \(L\), we investigate the quantitative properties of these sets under certain conditions using the uniqueness theorems of analytic functions.


Keywords


Eigenparameter; Spectral analysis; Eigenvalues; Spectral singularities; Discrete equation; Klein-Gordon equation

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v11i2.1328

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