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Article Dans Une Revue The Journal of Geometric Analysis Année : 2021

Toeplitz operators with analytic symbols

Résumé

We provide asymptotic formulas for the Bergman projector and Berezin-Toeplitz operators on a compact Kähler manifold. These objects depend on an integer N and we study, in the limit N → +∞, situations in which one can control them up to an error O(e^{-cN}) for some c > 0. We develop a calculus of Toeplitz operators with real-analytic symbols, which applies to Kähler man-ifolds with real-analytic metrics. In particular, we prove that the Bergman kernel is controlled up to O(e^{-cN}) on any real-analytic Kähler manifold as N → +∞. We also prove that Toeplitz operators with analytic symbols can be composed and inverted up to O(e^{-cN}). As an application, we study eigenfunction concentration for Toeplitz operators if both the manifold and the symbol are real-analytic. In this case we prove exponential decay in the classically forbidden region.
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Dates et versions

hal-01957594 , version 1 (17-12-2018)
hal-01957594 , version 2 (14-04-2020)

Identifiants

Citer

Alix Deleporte. Toeplitz operators with analytic symbols. The Journal of Geometric Analysis, 2021, 31, pp.3915-3967. ⟨10.1007/s12220-020-00419-w⟩. ⟨hal-01957594v2⟩
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