On the pseudogroup of local transformations commuting with a transversely elliptic operator and the existence of transverse metric

Abstract

The group of diffeomorphisms commuting with an elliptic operator on a manifold is a compact Lie group under Compact-Open topology. In foliation theory, pseudogroup is introduced by Sacksteder. The pseudogroup of local transformations commuting with a basic differential operator possesses the equicontinuity and the quasi-analyticity when conditions on operator are given. These properties serve to construct a transverse metric on the normal bundle under a good condition on operator. For this, the Average Method is applied as in the construction of basic connection on foliated bundles.

Somme corrections has been done followed by the advises of Mr.Alexandre Baldare. In the version 2, I have corrected some proofs, explained more in introduction and added more references