A general Simonenko local principle and Fredholm condition for isotypical components

TL;DR

This paper extends Simonenko's local principle to derive Fredholm criteria for isotypical components of invariant pseudodifferential operators, providing a comprehensive proof and relaxing previous assumptions.

Contribution

It offers a full proof of the equivariant local principle for isotypical components and broadens its applicability by relaxing earlier hypotheses.

Findings

Established Fredholm criteria for isotypical components

Provided a complete proof of the equivariant local principle

Extended the principle by relaxing previous assumptions

Abstract

In this paper, we derive, from a general Simonenko's local principle, Fredholm criteria for restriction to isotypical components. More precisely, we give a full proof, of the equivariant local principle for restriction to isotypical components of invariant pseudodifferential operators announced in \cite{BCLN2}. Furthermore, we extend this result by relaxing the hypothesis made in the preceding quoted paper.