Generators for the $C^m$-closures of ideals

Abstract

Let \mathscr{R} denote the ring of real polynomials on \mathbb{R}^{n} . Fix m\geq 0 , and let A_{1},\ldots,A_{M}\in\mathscr{R} . The C^{m} -closure of (A_{1},\ldots,A_{M}) , denoted here by [A_{1},\ldots,A_{M};C^{m}] , is the ideal of all f\in \mathscr{R} expressible in the form f=F_{1}A_{1}+\cdots +F_{M}A_{M} with each F_{i}\in C^{m}(\mathbb{R}^{n}) . In this paper we exhibit an algorithm for computing generators for [A_{1},\ldots,A_{M};C^{m}] .

Locations

• Revista Matemática Iberoamericana - View
• arXiv (Cornell University) - View - PDF