算子演算-外微分复形
Operator calculus - the exterior differential complex
摘要：
我们描述了构造为一列巴拿赫空间的归纳极限的微分形式的拓扑预对偶。这个子空间的电流有很好的性质，在狄拉克链和多面体链是密集的，其算子代数包含的运营商predual外导，霍奇星，李导，和内部产品。利用这些算子，我们建立了k-向量场在非光滑边界上净通量的高阶发散定理，开集上不一定正则的区域的Stokes定理，以及非光滑区域及其边界在光滑流中运动的一个新的基本定理.我们关闭广泛推广的莱布尼茨积分规则和Albertold的运输定理。
英文摘要：
We describe a topological predual to differential forms constructed as an inductive limit of a sequence of Banach spaces. This subspace of currents has nice properties, in that Dirac chains and polyhedral chains are dense, and its operator algebra contains operators predual to exterior derivative, Hodge star, Lie derivative, and interior product. Using these operators, we establish higher order divergence theorems for net flux of k-vector fields across nonsmooth boundaries, Stokes' theorem for domains in open sets which are not necessarily regular, and a new fundamental theorem for nonsmooth domains and their boundaries moving in a smooth flow. We close with broad generalizations of the Leibniz integral rule and Reynold's transport theorem.
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。
