Singular Bohr-Sommerfeld conditions for 1D Toeplitz operators: hyperbolic case

preprint2013arXivOpen access

Abstract

In this article, we state the Bohr-Sommerfeld conditions around a singular value of hyperbolic type of the principal symbol of a self-adjoint semiclassical Toeplitz operator on a compact connected Kähler surface. These conditions allow the description of the spectrum of the operator in a fixed size neighbourhood of the singularity. We provide numerical computations for three examples, each associated to a different topology.

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