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

Le Floch, Yohann

Anal. PDE 7, No. 7, 1595-1637 (2014).

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.

MSC:

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

Keywords:

semiclassical analysis; spectral theory; Toeplitz operators