Spectral Analysis of Klein-Gordon Difference Operator Given by a General Boundary Condition
DOI:
https://doi.org/10.26713/cma.v11i2.1328Keywords:
Eigenparameter, Spectral analysis, Eigenvalues, Spectral singularities, Discrete equation, Klein-Gordon equationAbstract
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 \(\{h_n\}^\infty_{n=1}\in l_1(\mathbb{N})\cap l_2(\mathbb{N})\). 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.
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