Fredholm Groupoids and Layer Potentials on Conical Domains

TL;DR

This paper demonstrates that layer potential groupoids for conical domains are Fredholm groupoids, providing a unified framework to analyze operators on singular spaces and establishing criteria for their Fredholm properties.

Contribution

It proves that layer potential groupoids for conical domains are Fredholm groupoids, enabling a unified approach to analysis on singular spaces.

Findings

Layer potential groupoids for conical domains are Fredholm groupoids.

Fredholm criteria for operators on these groupoids are established.

Unified treatment of analysis problems on singular spaces.

Abstract

We show that layer potential groupoids for conical domains constructed in an earlier paper (Carvalho-Qiao, Central European J. Math., 2013) are Fredholm groupoids, which enables us to deal with many analysis problems on singular spaces in a unified treatment. As an application, we obtain Fredholm criteria for operators on layer potential groupoids.