English

Nash regulous functions

Algebraic Geometry 2017-09-28 v1

Abstract

A real-valued function on R^n is k-regulous, where k is a nonnegative integer, if it is of class C^k and can be represented as a quotient of two polynomial functions on R^n. Several interesting results involving such functions have been obtained recently. Some of them (Nullstellensatz, Cartan's theorems A and B, etc.) can be carried over to a new setting of Nash regulous functions, introduced in this paper. Here a function on a Nash manifold X is called Nash k-regulous if it is of class C^k and can be represented as a quotient of two Nash functions on X.

Keywords

Cite

@article{arxiv.1709.09392,
  title  = {Nash regulous functions},
  author = {Wojciech Kucharz},
  journal= {arXiv preprint arXiv:1709.09392},
  year   = {2017}
}
R2 v1 2026-06-22T21:56:21.164Z