Modified classification of non-self-adjoint second-order difference equations

Abstract

This paper is concerned with the classification of non-self-adjoint second-order difference equations. The relationship between the number of summable solutions of non-self-adjoint difference equations and that of the discrete linear Hamiltonian system is discussed. A classification for non-self-adjoint second-order difference equations is established, which is independent of the choice of the rotated half plane and the fixed point.

Keywords:

• Weyl theory
• non-self-adjoint
• deficiency index
• limit point case
• limit circle case

AMS Subject Classifications:

• Primary: 34B20
• 47B39

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11301304], [grant number 11425105], [grant number 11571202]; General Financial Grant from the China Postdoctoral Science Foundation [grant number 2015M582069].