关于非线性广义函数II的基础
On the foundations of nonlinear generalized functions II
摘要：
本文对Colombeau型广义函数代数在第一部分中引入的同态不变商代数$\mathcal{G}^d = \mathcal{E}_M/\mathcal{N}$和Colombeau的原代数$\mathcal{G}^e$之间的范围进行了全面的分析。建立了三个主要结果：第一，给出了一个描述$\mathcal{N}$（适用于所有类型的Colombeau代数）中隶属关系的简单判据。第二，两个反例证明$\mathcal{G}^d$不是注射性地包含在$\mathcal{G}^e$中。最后，它表明，在范围“之间”$\mathcal{G}^d$和$\mathcal{G}^e$只有一个以上的建设导致一个同构不变代数。在分析后者，几个分类结果获得的内在描述$\mathcal{G}^d$流形上的必不可少的。
英文摘要：
This paper gives a comprehensive analysis of algebras of Colombeau-type generalized functions in the range between the diffeomorphism-invariant quotient algebra $\mathcal{G}^d = \mathcal{E}_M/\mathcal{N}$ introduced in part I and Colombeau's original algebra $\mathcal{G}^e$. Three main results are established: First, a simple criterion describing membership in $\mathcal{N}$ (applicable to all types of Colombeau algebras) is given. Second, two counterexamples demonstrate that $\mathcal{G}^d$ is not injectively included in $\mathcal{G}^e$. Finally, it is shown that in the range ``between'' $\mathcal{G}^d$ and $\mathcal{G}^e$ only one more construction leads to a diffeomorphism invariant algebra. In analyzing the latter, several classification results essential for obtaining an intrinsic description of $\mathcal{G}^d$ on manifolds are derived.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
