La teoria d'operadors pseudo-diferencials sobre les v-varietats i la seva relació amb les foliacions

The authors have developed the theory of pseudo-differential operators over a V-manifold (Here the difficult point is to give a good definition of a pseudo differential operator). The difficulty arise from the fact that pseudo-differential operators are not local and the groups that appear in the definition of a V-manifold are local. By applying this theory, the authors prove the existence of parametrices for elliptic differential operators of any order over a V-manifold and generalize some results from Reinhart concerning foliations with a bundle-like metric.