# ANNALES DE L'INSTITUT FOURIER

Une classe de symboles new-look
Annales de l'Institut Fourier, Volume 30 (1980) no. 3, pp. 199-217.

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.

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 ${\left(\frac{\partial }{\partial {x}_{n}}\right)}^{3}+{\sum }_{i=1}^{n-1}{\left(\frac{\partial }{\partial {x}_{i}}\right)}^{2}.$

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author = {Hirschowitz, Andr\'e},
title = {Une classe de symboles new-look},
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Hirschowitz, André. Une classe de symboles new-look. Annales de l'Institut Fourier, Volume 30 (1980) no. 3, pp. 199-217. doi : 10.5802/aif.798. https://aif.centre-mersenne.org/articles/10.5802/aif.798/

[1] L. Boutet De Monvel, Hypoelliptic operators with double characteristics and related pseudodifferential operators, Comm. Pure and Appl. Math., XXVII (1974), 585-639. | MR | Zbl

[2] J.J. Duistermaat, Fourier Integral Operators, Courant Institute of Math. Sciences, New York University, 1973. | MR | Zbl

[3] J.J. Duistermaat, Oscillatory Integrals, Lagrange Immersions and Unfolding of Singularities, Comm. Pure and Appl. Math., XXVII (1974), 207-281. | MR | Zbl

[4] J.J. Duistermaat, L. Hörmander, Fourier Integral Operators II, Acta Math., 128 (1972), 183-265. | MR | Zbl

[5] V. Guillemin, Singular Symbols, Preprint, 1975.

[6] B. Helffer, Invariants associés à une classe d'opd et applications à l'hypoellipticité, Ann. Inst. Fourier, XXVI Fasc. 2 (1976), 55-70. | Numdam | MR | Zbl

[7] L. Hörmander, Hypoelliptic differential operators, Ann. Inst. Fourier, XI (1961), 477-492. | Numdam | MR | Zbl

[8] L. Hörmander, Fourier Integral Operators I, Acta Math., 127 (1971), 79-183. | MR | Zbl

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