no. 2
On the eigenvalues of a class of hypo-elliptic operators. IV
Annales de l'Institut Fourier, Tome 30 (1980) no. 2, pp. 109-169

Let P be a selfadjoint classical pseudo-differential operator of order >1 with non-negative principal symbol on a compact manifold. We assume that P is hypoelliptic with loss of one derivative and semibounded from below. Then exp(-tP), t≥0, is constructed as a non-classical Fourier integral operator and the main contribution to the asymptotic distribution of eigenvalues of P is computed. This paper is a continuation of a series of joint works with A. Menikoff.

Soit P un opérateur pseudo-différentiel classique, d’ordre >1, de symbole principal non-négatif, sur une variété compacte. On suppose que P est hypoelliptique avec perte d’une dérivée et semi-borné inférieurement. On construit alors exp(-tP), t≥0 comme un opérateur intégral de Fourier non classique et on calcule la contribution principale à la distribution asymptotique des valeurs propres de P. Ce travail complète une série de travaux en collaboration avec A. Menikoff.

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Sjöstrand, Johannes. On the eigenvalues of a class of hypo-elliptic operators. IV. Annales de l'Institut Fourier, Tome 30 (1980) no. 2, pp. 109-169. doi: 10.5802/aif.788

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