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arXiv · 1809.06799

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

Yuri A. Kordyukov
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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 eigenfunctions 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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Yuri A. Kordyukov. 2020-02-05. Semiclassical spectral analysis of Toeplitz operators on symplectic manifolds: the case of discrete wells. https://doi.org/10.1007/s00209-020-02462-3

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