Mohammed Benalili
Azzedine Lansari

Spectral properties of the adjoint operator and applications

(Lobachevskii Journal of Mathematics, Vol.18, pp.33-51)

We present some spectral properties of the adjoint operator corresponding to some admissible dilatation vector field and some of its perturbations. Next, we apply these results via the Nash-Moser function inverse theorem to show that the group G of diffeomorphisms of the Euclidean space Rn which are 1-time flat, close to the identity and of small support acts transitively on the affine space of appropriate perturbations of the dilation vector field Xo.



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