Symmetric Solutions to Symmetric Partial Difference Equations
Classical Analysis and ODEs
2025-05-20 v3 Systems and Control
Systems and Control
Optimization and Control
Abstract
This paper studies systems of linear difference equations on the lattice that are invariant under a finite group of symmetries, and shows that there exist solutions to such systems that are also invariant under this group of symmetries.
Cite
@article{arxiv.2310.00903,
title = {Symmetric Solutions to Symmetric Partial Difference Equations},
author = {Shiva Shankar},
journal= {arXiv preprint arXiv:2310.00903},
year = {2025}
}
Comments
Theorem 4.2 in the earlier arxiv version does not charaterise all the symmetric solutions to a symmetric system of difference equations on $\Z^n,$ as claimed. Thus, the statement on the dimension of the space of symmetric solutions is an underestimate