Principal functions of nonselfadjoint discrete Dirac equations with spectral parameter in boundary conditions. (English) Zbl 1253.39005

Summary: Let \(L\) denote the operator generated in \(\ell_2(\mathbb N, \mathbb C^2)\) by \(a_{n+1}y^{(2)}_{n+1} + b_ny^{(2)}_n + p_ny^{(1)}_n = \lambda y^{(1)}_n, a_{n-1}y^{(1)}_{n-1} + b_ny^{(1)}_n + q_ny^{(2)}_n = \lambda y^{(2)}_n, n \in \mathbb N\), and the boundary condition \((\gamma_0 + \gamma_1 \lambda)y^{(2)}_1 + (\beta_0 + \beta_1 \lambda)y^{(1)}_0 = \mathbf{0}\), where \((a_n), (b_n), (p_n)\) and \((q_n), n \in \mathbb N\) are complex sequences, \(\gamma_i, \beta_i \in \mathbb C, i = 0, 1\), and \(\lambda\) is an eigenparameter. In this paper we investigated the principal functions corresponding to the eigenvalues and the spectral singularities of \(L\).


39A12 Discrete version of topics in analysis
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