On semiclassical and universal inequalities for eigenvalues of quantum graphs
Spectral Theory
2015-05-14 v1 Mathematical Physics
math.MP
Abstract
We study the spectra of quantum graphs with the method of trace identities (sum rules), which are used to derive inequalities of Lieb-Thirring, Payne-P\'olya-Weinberger, and Yang types, among others. We show that the sharp constants of these inequalities and even their forms depend on the topology of the graph. Conditions are identified under which the sharp constants are the same as for the classical inequalities; in particular, this is true in the case of trees. We also provide some counterexamples where the classical form of the inequalities is false.
Keywords
Cite
@article{arxiv.0911.1896,
title = {On semiclassical and universal inequalities for eigenvalues of quantum graphs},
author = {Semra Demirel and Evans M. Harrell},
journal= {arXiv preprint arXiv:0911.1896},
year = {2015}
}
Comments
18 pages