论文标题
哥伦布广泛数字的非库赛环中的高血压
Hyperseries in the non-Archimedean ring of Colombeau generalized numbers
论文作者
论文摘要
本文是本文的自然延续：Mukhammadiev A. Since the ring $\tilde{R}$ of Robinson-Colombeau is non-Archimedean, a classical series $\sum_{n=0}^{+\infty}a_{n}$ of generalized numbers $a_{n}\in\tilde{R}$ is convergent if and only if $a_{n}\to0$ in the sharp topology.因此，该特性不允许我们概括几个经典结果，主要是在研究广义函数的研究（例如，在整合一般函数集成中的Sigma-Additivity中）。引入高级概念，我们解决了这个问题，以恢复分析功能的经典示例以及几种经典结果。
This article is the natural continuation of the paper: Mukhammadiev A.~et al Supremum, infimum and hyperlimits of Colombeau generalized numbers in this journal. Since the ring $\tilde{R}$ of Robinson-Colombeau is non-Archimedean, a classical series $\sum_{n=0}^{+\infty}a_{n}$ of generalized numbers $a_{n}\in\tilde{R}$ is convergent if and only if $a_{n}\to0$ in the sharp topology. Therefore, this property does not permit us to generalize several classical results, mainly in the study of analytic generalized functions (as well as, e.g., in the study of sigma-additivity in integration of generalized functions). Introducing the notion of hyperseries, we solve this problem recovering classical examples of analytic functions as well as several classical results.
