Nash regulous functions

Wojciech Kucharz¹

¹ Institute of Mathematics Faculty of Mathematics and Computer Science Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland

Annales Polonici Mathematici, Tome 119 (2017) no. 3, pp. 275-289

Résumé

A real-valued function on $\mathbb {R}^n$ is $k$-regulous, where $k$ is a nonnegative integer, if it is of class $\mathcal {C}^k$ and can be represented as a quotient of two polynomial functions on $\mathbb {R}^n$. 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 $k$-regulous functions, introduced in this paper. Here a function on a Nash manifold $X$ is called Nash $k$-regulous if it is of class $\mathcal {C}^k$ and can be represented as a quotient of two Nash functions on $X$.

Détail

DOI : 10.4064/ap170601-21-8

Keywords: real valued function mathbb k regulous where nonnegative integer of class mathcal represented quotient polynomial functions mathbb several interesting results involving functions have obtained recently nullstellensatz cartan theorems nbsp nbsp etc carried setting nash k regulous functions introduced paper here nbsp function nash manifold called nash k regulous of class nbsp mathcal represented quotient nash functions nbsp