Non-degeneracy of the harmonic structure on Sierpinski Gaskets
Spectral Theory
2017-06-01 v3
Abstract
We prove that the harmonic extension matrices for the level-k Sierpinski Gasket are invertible for every k>2. This has been previously conjectured to be true by Hino in [6] and [7] and tested numerically for k<50. We also give a necessary condition for the non-degeneracy of the harmonic structure for general finitely ramified self-similar sets based on the vertex connectivity of their first graph approximation.
Keywords
Cite
@article{arxiv.1605.04117,
title = {Non-degeneracy of the harmonic structure on Sierpinski Gaskets},
author = {Konstantinos Tsougkas},
journal= {arXiv preprint arXiv:1605.04117},
year = {2017}
}
Comments
10 pages, 6 figures