JournalsrmiVol. 37, No. 3pp. 965–1006

Generators for the CmC^m-closures of ideals

  • Charles Fefferman

    Princeton University, USA
  • Garving K. Luli

    University of California at Davis, USA
Generators for the $C^m$-closures of ideals cover
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Abstract

Let R\mathscr{R} denote the ring of real polynomials on Rn\mathbb{R}^{n}. Fix m0m\geq 0, and let A1,,AMRA_{1},\ldots,A_{M}\in\mathscr{R}. The CmC^{m}-closure of (A1,,AM)(A_{1},\ldots,A_{M}), denoted here by [A1,,AM;Cm][A_{1},\ldots,A_{M};C^{m}], is the ideal of all fRf\in \mathscr{R} expressible in the form f=F1A1++FMAMf=F_{1}A_{1}+\cdots +F_{M}A_{M} with each FiCm(Rn)F_{i}\in C^{m}(\mathbb{R}^{n}). In this paper we exhibit an algorithm for computing generators for [A1,,AM;Cm][A_{1},\ldots,A_{M};C^{m}].

Cite this article

Charles Fefferman, Garving K. Luli, Generators for the CmC^m-closures of ideals. Rev. Mat. Iberoam. 37 (2021), no. 3, pp. 965–1006

DOI 10.4171/RMI/1218