Spectral Analysis of Klein-Gordon Difference Operator Given by a General Boundary Condition - Yokus, Nihal; Coskun, Nimet (Communications in Mathematics and Applications, 2020)
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 $$ Δ (a_{n-1}Δ y_{n-1})+(v_n-λ)^2y_n=0, \ \ n \in \mathbb{N},$$ and a general boundary condition $$\sum^∞_{n=0} h_ny_n=0,$$ where \(a_0 = 1\), \(h_0 eq 0\) and \(\{a_n\}^∞_{n=1}\), \(\{v_n\}^∞_{n=1}\) and \(\{h_n\}^∞_{n=1}\) are complex sequences and \(\{h_n\}^∞_{n=1}\in l_1(\mathbb{N})\cap l_2(\mathbb{N})\). 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.
Keywords: Eigenparameter; Spectral analysis; Eigenvalues; Spectral singularities; Discrete equation; Klein-Gordon equation