Asymptotic ideals (ideals in the ring of Colombeau generalized constants with continuous parametrization)
Rings and Algebras
2014-04-01 v1 Functional Analysis
Abstract
We study the asymptotics at zero of continuous functions on (0, 1] by means of their asymptotic ideals, i.e., ideals in the ring of continuous functions on (0, 1] satisfying a polynomial growth condition at 0 modulo rapidly decreasing functions at 0. As our main result, we characterize maximal and prime ideals in terms of maximal and prime filters.
Keywords
Cite
@article{arxiv.1210.5634,
title = {Asymptotic ideals (ideals in the ring of Colombeau generalized constants with continuous parametrization)},
author = {Anatole Khelif and Dimitris Scarpalezos and Hans Vernaeve},
journal= {arXiv preprint arXiv:1210.5634},
year = {2014}
}
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19 pages