On the full calculus of pseudo-differential operators on boundary   groupoids with polynomial growth
  In this paper, we enlarge the space of uniformly supported pseudo-differential operators on some groupoids by considering kernels satisfying certain asymptotic estimates. We show that such enlarged space contains the compact parametrix, and the generalized inverse of uniformly supported operators with Fredholm vector representation. 
Bing Kwan So
math.AP math.DG