Hairer's Reconstruction Theorem without Regularity Structures

Francesco Caravenna, Lorenzo Zambotti

Published 2020-05-19Version 1

This survey is devoted to Martin Hairer's Reconstruction Theorem, which is one of the cornerstones of his theory of Regularity Structures. Our aim is to give a new self-contained and elementary proof of this Theorem and of some applications. We present it as a general result in the theory of distributions that can be understood without any knowledge of Regularity Structures themselves, which we do not even need to define.