English

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.

Keywords

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}
}
R2 v1 2026-06-21T11:45:39.352Z