Vol. 7, No. 7, 2014

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Singular Bohr–Sommerfeld conditions for 1D Toeplitz operators: hyperbolic case

Yohann Le Floch

Vol. 7 (2014), No. 7, 1595–1637
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