Semiclassical spectral estimates for Toeplitz operators
Annales de l'Institut Fourier, Volume 48 (1998) no. 4, pp. 1189-1229.

Let X be a compact Kähler manifold with integral Kähler class and LX a holomorphic Hermitian line bundle whose curvature is the symplectic form of X. Let HC (X,) be a Hamiltonian, and let T k be the Toeplitz operator with multiplier H acting on the space k =H 0 (X,L k ). We obtain estimates on the eigenvalues and eigensections of T k as k, in terms of the classical Hamilton flow of H. We study in some detail the case when X is an integral coadjoint orbit of a Lie group.

Soit X une variété kählérienne compacte de classe de Kähler entière et LX un fibré en droites hermitien holomorphe, dont la courbure est la forme symplectique sur X. Soit HC (X,) un hamiltonien et T k l’opérateur de Toeplitz de multiplicateur H agissant sur l’espace k =H 0 (X,L k ). On obtient des estimations sur les valeurs et fonctions propres de T k lorsque k en termes du flot hamiltonien associé a H. On étudie en détail le cas où X est une orbite coadjointe entière d’un groupe de Lie.

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     title = {Semiclassical spectral estimates for {Toeplitz} operators},
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Borthwick, David; Paul, Thierry; Uribe, Alejandro. Semiclassical spectral estimates for Toeplitz operators. Annales de l'Institut Fourier, Volume 48 (1998) no. 4, pp. 1189-1229. doi : 10.5802/aif.1654. http://archive.numdam.org/articles/10.5802/aif.1654/

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