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Asymptotic ideals (ideals in the ring of Colombeau generalized constants with continuous parametrization)

(2014) COMMUNICATIONS IN ALGEBRA. 42(6). p.2721-2739
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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
Asymptotic analysis, Filter, Algebra of continuous functions, Algebra of generalized functions, Maximal ideal, NUMBERS

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Citation

Please use this url to cite or link to this publication:

Chicago
Khelif, A, D Scarpalezos, and Hans Vernaeve. 2014. “Asymptotic Ideals (ideals in the Ring of Colombeau Generalized Constants with Continuous Parametrization).” Communications in Algebra 42 (6): 2721–2739.
APA
Khelif, A., Scarpalezos, D., & Vernaeve, H. (2014). Asymptotic ideals (ideals in the ring of Colombeau generalized constants with continuous parametrization). COMMUNICATIONS IN ALGEBRA, 42(6), 2721–2739.
Vancouver
1.
Khelif A, Scarpalezos D, Vernaeve H. Asymptotic ideals (ideals in the ring of Colombeau generalized constants with continuous parametrization). COMMUNICATIONS IN ALGEBRA. 2014;42(6):2721–39.
MLA
Khelif, A, D Scarpalezos, and Hans Vernaeve. “Asymptotic Ideals (ideals in the Ring of Colombeau Generalized Constants with Continuous Parametrization).” COMMUNICATIONS IN ALGEBRA 42.6 (2014): 2721–2739. Print.
@article{6845417,
  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.},
  author       = {Khelif, A and Scarpalezos, D and Vernaeve, Hans},
  issn         = {0092-7872},
  journal      = {COMMUNICATIONS IN ALGEBRA},
  keyword      = {Asymptotic analysis,Filter,Algebra of continuous functions,Algebra of generalized functions,Maximal ideal,NUMBERS},
  language     = {eng},
  number       = {6},
  pages        = {2721--2739},
  title        = {Asymptotic ideals (ideals in the ring of Colombeau generalized constants with continuous parametrization)},
  url          = {http://dx.doi.org/10.1080/00927872.2013.772189},
  volume       = {42},
  year         = {2014},
}

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