Constructing discrete harmonic functions in wedges
Spectral Theory
2023-01-19 v2 Functional Analysis
Probability
Abstract
We propose a systematic construction of signed harmonic functions for discrete Laplacian operators with Dirichlet conditions in the quarter plane. In particular, we prove that the set of harmonic functions is an algebra generated by a single element, which conjecturally corresponds to the unique positive harmonic function.
Cite
@article{arxiv.2012.08947,
title = {Constructing discrete harmonic functions in wedges},
author = {Viet Hung Hoang and Kilian Raschel and Pierre Tarrago},
journal= {arXiv preprint arXiv:2012.08947},
year = {2023}
}
Comments
42 pages, 8 figures