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

Yohann Le Floch (1, 2)

1 School of Mathematical Sciences
2 IRMAR - Institut de Recherche Mathématique de Rennes

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 K\"{a}hler 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.

Mots clés: semiclassical analysis; spectral theory; Toeplitz operators

Domaines: Théorie spectrale [math.SP]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Yohann Le Floch. Singular Bohr-Sommerfeld conditions for 1D Toeplitz operators: hyperbolic case. Analysis & PDE, 2014, 7 (7), pp.1595-1637. ⟨10.2140/apde.2014.7.1595⟩. ⟨hal-00864296⟩