The converse of Sturm's Separation Theorem
Classical Analysis and ODEs
2021-09-16 v1 Spectral Theory
Abstract
We show that Sturm's classical separation theorem on the interlacing of the zeros of linearly independent solutions of real second order two-term ordinary differential equations necessarily fails in the presence of a unique turning point in the principal part of the equation. Related results are discussed. The last section contains an extension of the main result to a finite number of turning points.
Keywords
Cite
@article{arxiv.2109.06953,
title = {The converse of Sturm's Separation Theorem},
author = {L. Gholizadeh and A. B. Mingarelli},
journal= {arXiv preprint arXiv:2109.06953},
year = {2021}
}
Comments
9 pages. The first 4 sections of this appear will appear separately