Extension of functions with bounded finite differences
Differential Geometry
2008-11-27 v1
Abstract
We prove that functions defined on a lattice in a finite dimensional torus with bounded finite differences can be smoothly extended to the whole torus, and relate the bounds on the extension's derivatives with bounds on the original function's finite differences.
Cite
@article{arxiv.0811.4366,
title = {Extension of functions with bounded finite differences},
author = {P. Duarte and M. J. Torres},
journal= {arXiv preprint arXiv:0811.4366},
year = {2008}
}