OPTIMAL EMBEDDINGS OF DISTRIBUTIONS INTO ALGEBRAS

Proceedings of the Edinburgh Mathematical Society

H. Vernaeve¹ 

关键词: generalized functions;    distributions;    embeddings;    injective modules;    Colombeau;   

DOI  :  10.1017/S0013091500001188

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let $varOmega$ be a convex, open subset of $mathbb{R}^n$ and let $mathcal{D}'(varOmega)$ be the space of distributions on $varOmega$. It is shown that there exist linear embeddings of $mathcal{D}'(varOmega)$ into a differential algebra that commute with partial derivatives and that embed $mathcal{C}^{infty}(varOmega)$ as a subalgebra. This embedding appears to be the first one after Colombeau’s to possess these properties. We show that many nonlinear operations on distributions can be defined that are not definable in the Colombeau setting.AMS 2000 Mathematics subject classification: Primary 46F30. Secondary 13C11

【 授权许可】

Unknown