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

Le Floch, Yohann

doi:10.2140/apde.2014.7.1595

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

Yohann Le Floch

Vol. 7 (2014), No. 7, 1595–1637

DOI: 10.2140/apde.2014.7.1595

Abstract

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.

Keywords

semiclassical analysis, spectral theory, Toeplitz operators

Mathematical Subject Classification 2010

Primary: 58J50

Secondary: 53D50, 81S10, 35P20

Milestones

Received: 23 September 2013

Revised: 7 July 2014

Accepted: 19 August 2014

Published: 12 December 2014

Authors

Yohann Le Floch
School of Mathematical Sciences Tel Aviv University Ramat Aviv Tel Aviv 6997801 Israel

Vol. 7, No. 7, 2014