Measure-geometric Laplacians for discrete distributions
Dynamical Systems
2021-12-02 v2 Functional Analysis
Spectral Theory
Abstract
In 2002 Freiberg and Z\"ahle introduced and developed a harmonic calculus for measure-geometric Laplacians associated to continuous distributions. We show their theory can be extended to encompass distributions with finite support and give a matrix representation for the resulting operators. In the case of a uniform discrete distribution we make use of this matrix representation to explicitly determine the eigenvalues and the eigenfunctions of the associated Laplacian.
Cite
@article{arxiv.1702.03873,
title = {Measure-geometric Laplacians for discrete distributions},
author = {Marc Kesseböhmer and Tony Samuel and Hendrik Weyer},
journal= {arXiv preprint arXiv:1702.03873},
year = {2021}
}
Comments
8 pages, 4 figures