论文标题
超功率系列和广义的真实分析功能
Hyper-power series and generalized real analytic functions
论文作者
论文摘要
本文是Tiwari，D.，Giordano，P。的自然延续，《哥伦布非安置式哥伦布戒指》中的高级文章在本期刊中。我们通过分析收敛半径的概念，并证明经典结果，例如代数操作，组成和倒数量，我们研究了一个可变的超功率序列。然后，我们定义和研究一个可变的广义实际分析函数，考虑到它们的衍生，整合，适当的身份定理表述以及在功能紧凑的集合上衍生物的均匀上限的表征。相反，在哥伦布实际分析功能理论中的经典使用序列使用，我们可以在非限时收敛集中恢复几个经典示例。广义真实分析功能的概念表明，相对于经典的概念和哥伦布理论，例如包括具有平坦点和几个分布（例如Dirac Delta）的经典非分析平滑函数。另一方面，每个哥伦布实际分析函数也是广义的实际分析函数。
This article is a natural continuation of the paper Tiwari, D., Giordano, P., Hyperseries in the non-Archimedean ring of Colombeau generalized numbers in this journal. We study one variable hyper-power series by analyzing the notion of radius of convergence and proving classical results such as algebraic operations, composition and reciprocal of hyper-power series. We then define and study one variable generalized real analytic functions, considering their derivation, integration, a suitable formulation of the identity theorem and the characterization by uniform upper bounds of derivatives on functionally compact sets. On the contrary with respect to the classical use of series in the theory of Colombeau real analytic functions, we can recover several classical examples in a non-infinitesimal set of convergence. The notion of generalized real analytic function reveals to be less rigid both with respect to the classical one and to Colombeau theory, e.g. including classical non-analytic smooth functions with flat points and several distributions, such as the Dirac delta. On the other hand, each Colombeau real analytic function is also a generalized real analytic function.
