ASYMPTOTIC IDEALS (IDEALS IN THE RING OF COLOMBEAU GENERALIZED CONSTANTS WITH CONTINUOUS PARAMETRIZATION)

作者：Khelif A; Scarpalezos D; Vernaeve H^*

来源：Communications in Algebra, 2014, 42(6): 2721-2739.

DOI：10.1080/00927872.2013.772189

• Algebra of continuous functions
• Algebra of generalized functions
• Asymptotic analysis
• Filter
• Maximal ideal

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.

• 出版日期2014-6-3