A General Simonenko Local Principle and Fredholm Condition for Isotypical Components

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 Baldare et al. (Muenster J Math, 2021). Furthermore, we extend this result by relaxing the hypothesis made in the preceding quoted paper.