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Semiclassical spectral analysis of Toeplitz operators on symplectic manifolds: the case of discrete wells

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Abstract

We consider Toeplitz operators associated with the renormalized Bochner Laplacian on high tensor powers of a positive line bundle on a compact symplectic manifold. We study the asymptotic behavior, in the semiclassical limit, of low-lying eigenvalues and the corresponding eigensections of a self-adjoint Toeplitz operator under assumption that its principal symbol has a non-degenerate minimum with discrete wells. As an application, we prove upper bounds for low-lying eigenvalues of the Bochner Laplacian in the semiclassical limit.

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Authors and Affiliations

  1. Institute of Mathematics with Computing Centre, Ufa Federal Research Centre of Russian Academy of Sciences, 112 Chernyshevsky str., 450008, Ufa, Russia

    Yuri A. Kordyukov

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  1. Yuri A. Kordyukov
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Kordyukov, Y.A. Semiclassical spectral analysis of Toeplitz operators on symplectic manifolds: the case of discrete wells. Math. Z. 296, 911–943 (2020). https://doi.org/10.1007/s00209-020-02462-3

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  • DOI: https://doi.org/10.1007/s00209-020-02462-3

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