Non-selfadjoint Finite System of Discrete Sturm-Liouville Operators with Hyperbolic Eigenparameter

Abstract

In this paper, spectrum and spectral properties of the operator generated by the finite system of Sturm-Liouville discrete equations with hyperbolic eigenparameter have been taken under investigation. The transformation choosen for the eigenparameter affects drastically the representation of Jost solution and analicity region of the Jost function. Besides obtaining resolvent operator of the problem, finiteness of the eigenvalues and spectral singularities have been proved by using the analicity of the Jost solution on the complex left half-plane. Hence, generalizing the recent results, this paper lays the groundwork for future research questions in different branches of science like inverse scattering theory, quantum physics, applied mathematics and etc.

Keywords

• discrete equations;
• spectral analysis;
• eigenvalues;
• spectral singularities

References

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