An uncertainty principle and lower bounds for the Dirichlet Laplacian on graphs
Functional Analysis
2018-04-02 v2
Abstract
We prove a quantitative uncertainty principle at low energies for the Laplacian on fairly general weighted graphs with a uniform explicit control of the constants in terms of geometric quantities. A major step consists in establishing lower bounds for Dirichlet eigenvalues in terms of the geometry.
Keywords
Cite
@article{arxiv.1606.07476,
title = {An uncertainty principle and lower bounds for the Dirichlet Laplacian on graphs},
author = {Daniel Lenz and Peter Stollmann and Gunter Stolz},
journal= {arXiv preprint arXiv:1606.07476},
year = {2018}
}
Comments
28 pages; minor revision, some (Counter)examples added, to appear in: Journal of Spectral Theory