## 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
R^{n} 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 X_{o}.

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