부산대학교 도서관

Let M be a smooth manifold, I⊂Mt∈D′(U\I)D′(U) 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 I⊂Mt∈D′(U\I)D′(U) to admit an extension in I⊂Mt∈D′(U\I)D′(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.