Asymptotic spectral analysis of Toeplitz operators on symplectic manifolds

Jeudi 24 mai 2018 15:45-16:45 - Yuri Kordyukov - Russian Academy of Sciences

Résumé : We describe the algebra of Toeplitz operators on a quantizable compact symplectic manifold associated with the renormalized Bochner Laplacian of a prequantum line bundle. This algebra provides a Berezin-Toeplitz type quantization of the symplectic manifold. It can also be considered as a generalization of the algebra of pseudodifferential operators. We discuss some asymptotic spectral properties of Toeplitz operators such as asymptotic behavior of low-lying eigenvalues and localization of the corresponding eigenfunctions, as well as applications to the spectral theory of the Bochner Laplacian.

Lieu : IMO, Salle 3L8

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