Besov Reconstruction
Besov Reconstruction
复制标题
别索夫重建
作者：
Lucas Broux;David Lee
重构定理解决了在ℝd$mathbb{R}^{d}上或在流形上为给定的充分相干局部逼近族建立全局分布的问题。这个定理是海尔正则性结构理论中的一个重要工具。本文建立了Besov集上的一个重构定理，推广了Carvenna和Zambotti的最新结果。Besov重构定理首先是由Hairer和Labbé在正则性结构的背景下，利用小波分析的非平凡结果提出的。我们的计算遵循Carvenna和Zambotti关于相干细菌的更基本的方法。有了这个公式，我们的结果既可以用分布论的工具来陈述和证明，又不需要正则性结构理论。作为应用，我们给出了一个不需要使用拟微积分的(Besov)Young乘法定理的另一种证明。
The reconstruction theorem tackles the problem of building a global distribution, on ℝ d $mathbb {R}^{d}$ or on a manifold, for a given family of sufficiently coherent local approximations. This theorem is a critical tool within Hairer’s theory of Regularity Structures. In this paper, we establish a reconstruction theorem in the Besov setting, extending recent results of Caravenna and Zambotti. A Besov reconstruction theorem was first formulated by Hairer and Labbé in the context of regularity structures, exploiting nontrivial results from wavelet analysis. Our calculations follow the more elementary approach of coherent germs due to Caravenna and Zambotti. With this formulation our results are both stated and proved with tools from the theory of distributions without the need of the theory of Regularity Structures. As an application, we present an alternative proof of a (Besov) Young multiplication theorem which does not require the use of para-differential calculus.
贝索夫粗略路径分析
影响因子：
2.4
作者：
Friz, Peter K.;Seeger, Benjamin;Zorin-Kranich, Pavel
通讯作者：
Zorin-Kranich, Pavel