Let be a compact Kähler manifold with integral Kähler class and a holomorphic Hermitian line bundle whose curvature is the symplectic form of . Let be a Hamiltonian, and let be the Toeplitz operator with multiplier acting on the space . We obtain estimates on the eigenvalues and eigensections of as , in terms of the classical Hamilton flow of . We study in some detail the case when is an integral coadjoint orbit of a Lie group.
Soit une variété kählérienne compacte de classe de Kähler entière et un fibré en droites hermitien holomorphe, dont la courbure est la forme symplectique sur . Soit un hamiltonien et l’opérateur de Toeplitz de multiplicateur agissant sur l’espace . On obtient des estimations sur les valeurs et fonctions propres de lorsque en termes du flot hamiltonien associé a . On étudie en détail le cas où est une orbite coadjointe entière d’un groupe de Lie.
@article{AIF_1998__48_4_1189_0, 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}, zbl = {0920.58059}, mrnumber = {2000c:58048}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1654/} }
TY - JOUR AU - Borthwick, David AU - Paul, Thierry AU - Uribe, Alejandro TI - Semiclassical spectral estimates for Toeplitz operators JO - Annales de l'Institut Fourier PY - 1998 SP - 1189 EP - 1229 VL - 48 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1654/ DO - 10.5802/aif.1654 LA - en ID - AIF_1998__48_4_1189_0 ER -
%0 Journal Article %A Borthwick, David %A Paul, Thierry %A Uribe, Alejandro %T Semiclassical spectral estimates for Toeplitz operators %J Annales de l'Institut Fourier %D 1998 %P 1189-1229 %V 48 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1654/ %R 10.5802/aif.1654 %G en %F AIF_1998__48_4_1189_0
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. https://aif.centre-mersenne.org/articles/10.5802/aif.1654/
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