重构定理的一个初等证明
An elementary proof of the reconstruction theorem
摘要：
重建定理是Martin Hairer正则性结构理论的基石，在本文中作为光滑模型集上明确给出的重建算子的唯一扩展而出现，这是由于其固有的Lipschitz性质。这个新的证明是一个直接后果的建设的软化程序的空间模型和建模的分布：更准确地说，对于一个抽象的模型$Z$的一个给定的规则性结构，一个软化的模型被构造，此外，任何建模的分布$f$可以近似的元素的通用子空间的建模的分布空间。这些考虑产生特别是粗糙路径理论的非标准近似结果。所有结果均在通用$(p,q)$ Besov设置中制定。
英文摘要：
The reconstruction theorem, a cornerstone of Martin Hairer's theory of regularity structures, appears in this article as the unique extension of the explicitly given reconstruction operator on the set of smooth models due its inherent Lipschitz properties. This new proof is a direct consequence of constructions of mollification procedures on spaces of models and modelled distributions: more precisely, for an abstract model $Z$ of a given regularity structure, a mollified model is constructed, and additionally, any modelled distribution $f$ can be approximated by elements of a universal subspace of modelled distribution spaces. These considerations yield in particular a non-standard approximation results for rough path theory. All results are formulated in a generic $(p,q)$ Besov setting.
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