On the eigenvalues of a class of hypo-elliptic operators. IV
Annales de l'Institut Fourier, Volume 30 (1980) no. 2, p. 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), t0, 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), t0 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.

@article{AIF_1980__30_2_109_0,
     author = {Sj\"ostrand, Johannes},
     title = {On the eigenvalues of a class of hypo-elliptic operators. IV},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {30},
     number = {2},
     year = {1980},
     pages = {109-169},
     doi = {10.5802/aif.788},
     zbl = {0417.47024},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1980__30_2_109_0}
}
Sjöstrand, Johannes. On the eigenvalues of a class of hypo-elliptic operators. IV. Annales de l'Institut Fourier, Volume 30 (1980) no. 2, pp. 109-169. doi : 10.5802/aif.788. http://www.numdam.org/item/AIF_1980__30_2_109_0/

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