Singular Bohr-Sommerfeld conditions for 1D Toeplitz operators: hyperbolic case. (English) Zbl 1304.47039

Summary: We state the Bohr-Sommerfeld conditions around a singular value of hyperbolic type of the principal symbol of a selfadjoint semiclassical Toeplitz operator on a compact connected Riemann surface. These conditions allow the description of the spectrum of the operator in a fixed-size neighborhood of the singularity. We provide numerical computations for three examples, each associated with a different topology.


47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
53D50 Geometric quantization
81S10 Geometry and quantization, symplectic methods
35P20 Asymptotic distributions of eigenvalues in context of PDEs
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