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

Soit X une variété kählérienne compacte de classe de Kähler entière et L→X un fibré en droites hermitien holomorphe, dont la courbure est la forme symplectique sur X. Soit H∈C ∞ (X,ℝ) un hamiltonien et T k l’opérateur de Toeplitz de multiplicateur H agissant sur l’espace ℋ 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.

Let X be a compact Kähler manifold with integral Kähler class and L→X a holomorphic Hermitian line bundle whose curvature is the symplectic form of X. Let H∈C ∞ (X,ℝ) be a Hamiltonian, and let T k be the Toeplitz operator with multiplier H acting on the space ℋ 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.

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     author = {Borthwick, David and Paul, Thierry and Uribe, Alejandro},
     title = {Semiclassical spectral estimates for {Toeplitz} operators},
     journal = {Annales de l'Institut Fourier},
     pages = {1189--1229},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {48},
     number = {4},
     year = {1998},
     doi = {10.5802/aif.1654},
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     mrnumber = {2000c:58048},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1654/}
}
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Borthwick, David; Paul, Thierry; Uribe, Alejandro. Semiclassical spectral estimates for Toeplitz operators. Annales de l'Institut Fourier, Tome 48 (1998) no. 4, pp. 1189-1229. doi : 10.5802/aif.1654. https://aif.centre-mersenne.org/articles/10.5802/aif.1654/

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