Applying the index theorem to non-smooth operators

TL;DR

This paper introduces a method to extend index-theoretic results from smooth differential operators to those with less regular coefficients of finite Sobolev order, broadening the applicability of index theory.

Contribution

It provides a straightforward approach to generalize index theorems to non-smooth operators with Sobolev regularity, filling a gap in the existing theory.

Findings

Extended index theorems to operators with Sobolev coefficients

Simplified the process of applying index theory to non-smooth operators

Broadened the class of operators for which index results are valid

Abstract

We give a simple way to extend index-theoretical statements from partial differential operators with smooth coefficients to operators with coefficients of finite Sobolev order.