The positive and negative deficiency indices of formally self-adjoint difference equations
Classical Analysis and ODEs
2021-09-13 v1
Abstract
This paper is concerned with formally self-adjoint difference equations and their positive and negative deficiency indices. It is shown that the order of any formally self-adjoint difference equation is even, and some characterizations of formally self-adjoint difference equations are established. Further, we show that the positive and negative deficiency indices are always equal, which implies the existence of the self-adjoint extensions of the minimal linear relations generated by the difference equations. This is an important and essential difference between formally self-adjoint difference equations and their corresponding differential equations in the spectral theory.
Keywords
Cite
@article{arxiv.2109.04679,
title = {The positive and negative deficiency indices of formally self-adjoint difference equations},
author = {Guojing Ren},
journal= {arXiv preprint arXiv:2109.04679},
year = {2021}
}