## Étude du spectre pour un opérateur globalement elliptique dont le symbole de Weyl présente des symétries. I: Action des groupes finis. (Study of the spectrum of a global elliptic operator whose Weyl symbol shows symmetries. I: Action of finite groups).(French)Zbl 0583.58029

The authors study the spectrum of a global elliptic pseudo-differential operator Q, whose Weyl symbol is invariant under the action of a finite group G. To each irreducible character $$\chi$$ of G there corresponds a projection P of $$L^ 2({\mathbb{R}}^ n)$$ such that $$[Q,P]=0$$. They estimate the asymptotic distribution of the eigenvalues of $$Q|_{Im P}$$ in terms of $$\chi$$ and the distribution of the eigenvalues of Q.
Reviewer: J.Marschall

### MSC:

 58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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