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

TL;DR

This paper extends the class of pseudo-differential operators on boundary groupoids with polynomial growth by including kernels with specific asymptotic behaviors, enabling the construction of parametrices and generalized inverses.

Contribution

It introduces an enlarged space of operators with asymptotic kernel estimates, broadening the analytical tools available for boundary groupoids.

Findings

Enlarged operator space contains compact parametrices.

Generalized inverses exist for certain Fredholm operators.

Operators with asymptotic kernels are effectively analyzed.

Abstract

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.