Dirichlet eigenvalues of the Laplacian on full one-sided shift space
Dynamical Systems
2019-09-09 v1
Abstract
The full one sided shift space over finite symbols is approximated by an increasing sequence of finite subsets of the space. The Laplacian on the space is then defined as a renormalised limit of the difference operators defined on these subsets. In this work, we determine the spectrum of these difference operators completely, using the method of spectral decimation. Further, we prove that under certain conditions, the renormalised eigenvalues of the difference operators converge to an eigenvalue of the Laplacian.
Cite
@article{arxiv.1909.02784,
title = {Dirichlet eigenvalues of the Laplacian on full one-sided shift space},
author = {Shrihari Sridharan and Sharvari Neetin Tikekar},
journal= {arXiv preprint arXiv:1909.02784},
year = {2019}
}