Spectral properties of a finite system of Sturm–Liouville difference operators

Abstract

Let L denote the difference operator generated in by the system of the difference expressions

where and are complex sequences. In this paper, we investigated the spectrum, the spectral singularities, and properties of the principal vectors corresponding to the spectral singularities of L.

Keywords:

• eigenvalues
• eigenfunctions
• spectral singularities
• principal functions
• resolvent

2000 Mathematics Subject Classification::

• 58C40
• 34L05
• 34L40

Acknowledgement

The author would like to thank Professor E. Bairamov for his helpful suggestions during the preparation of this work.