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 gave a full proof, of the equivariant local principle for restriction to isotypical components of invariant pseudodifferential operators announced in [11]. Furthermore, we extend this result by relaxing the hypothesis made in the preceding quoted paper.