The extension of distributions on manifolds, a microlocal approach
- Resource Type
- Working Paper
- Authors
- Dang, Nguyen Viet
- Source
- Subject
- Mathematical Physics
81T20 35A18 46F12
- Language
Let $M$ be a smooth manifold, $I\subset M$ a closed embedded submanifold of $M$ and $U$ an open subset of $M$. In this paper, we find conditions using a geometric notion of scaling for $t\in \mathcal{D}^\prime(U\setminus I)$ to admit an extension in $\mathcal{D}^\prime(U)$. We give microlocal conditions on $t$ which allow to control the wave front set of the extension generalizing a previous result of Brunetti--Fredenhagen. Furthermore, we show that there is a subspace of extendible distributions for which the wave front of the extension is minimal which has applications for the renormalization of quantum field theory on curved spacetimes.
Comment: The main extension Theorem generalizes the result of the author's Phd thesis