Approximation of fractals by discrete graphs: norm resolvent and spectral convergence
Spectral Theory
2018-09-10 v2 Mathematical Physics
Functional Analysis
math.MP
Abstract
We show a norm convergence result for the Laplacian on a class of post-critically finite fractals with arbitrary Borel regular probability measure which can be approximated by a sequence of finite-dimensional graph Laplacians with corresponding discrete probability measures. As a consequence other functions of the Laplacians (heat operator, spectral projections etc.) converge as well in operator norm. One also deduces convergence of the spectrum and the eigenfunctions in energy norm.
Cite
@article{arxiv.1704.00064,
title = {Approximation of fractals by discrete graphs: norm resolvent and spectral convergence},
author = {Olaf Post and Jan Simmer},
journal= {arXiv preprint arXiv:1704.00064},
year = {2018}
}
Comments
now 24 pages, 2 figures