Une classe de symboles new-look

Hirschowitz, André

Annales de l'Institut Fourier, Tome 30 (1980) no. 3, pp. 199-217

On construit par voie géométrique une classe de symboles classiques en dehors d’une sous-variété. La classe d’opérateurs pseudodifférentiels associée contient les paramétrix d’opérateurs tels que ${\sum }_{i=1}^{n-1}{\left(\frac{\partial }{\partial x_i}\right)}^4+{\left(\frac{\partial }{\partial x_n}\right)}^3$ ou ${\left(\frac{\partial }{\partial x_n}\right)}^3+{\sum }_{i=1}^{n-1}{\left(\frac{\partial }{\partial x_i}\right)}^2.$

We construct, in a geometric way, a class of symbols which are classical except along some submanifold. The parametrics of ${\sum }_{i=1}^{n-1}{\left(\frac{\partial }{\partial x_i}\right)}^4+{\left(\frac{\partial }{\partial x_n}\right)}^3$ and ${\left(\frac{\partial }{\partial x_n}\right)}^3+{\sum }_{i=1}^{n-1}{\left(\frac{\partial }{\partial x_i}\right)}^2$, for instance, belong to the associated class of pseudodifferential operators.

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