Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure
Spectral Theory
2018-04-24 v1 Analysis of PDEs
Functional Analysis
Abstract
In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds can not be established.
Keywords
Cite
@article{arxiv.1804.08353,
title = {Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure},
author = {Bobo Hua and Matthias Keller and Michael Schwarz and Melchior Wirth},
journal= {arXiv preprint arXiv:1804.08353},
year = {2018}
}