On the full calculus of pseudo-differential operators on boundary groupoids with polynomial growth (Q1946785)

Most mathematicians study differential operators on manifolds with boundary. This paper is related to pseudo-differential operators on boundary groupoids which is an application of the manifolds with boundary. Firstly, the author defines the concept of boundary groupoid which is a special case of Lie groupoids. More precisely, the boundary groupoids are b-stretched products with possibly non-commutative isotropy subgroups and more degenerate Lie algebroids. The author constructs the generalized inverse of uniformly supported pseudo-differential operators, or elliptic operators, on boundary groupoids with polynomial growth. For it, he is using the kernels satisfying certain asymptotic estimates and von Neumann series.