A Hilbert space on left-definite Sturm-Liouville difference equation
Classical Analysis and ODEs
2015-05-26 v1 Analysis of PDEs
Functional Analysis
Abstract
We investigate the discrete Sturm-Liouville equations. In the present situation, the right hand side of the equation does not give rise to a positive definite quadratic form and we use instead the left hand side to define such a form. We prove in this paper that this form determines a Hilbert space (such problems are called left-definite).
Cite
@article{arxiv.1505.06517,
title = {A Hilbert space on left-definite Sturm-Liouville difference equation},
author = {Rami AlAhmad},
journal= {arXiv preprint arXiv:1505.06517},
year = {2015}
}