# Semiclassical inverse spectral theory for singularities of focus-focus type

We prove, assuming that the Bohr-Sommerfeld rules hold, that the joint spectrum near a focus-focus critical value of a quantum integrable system determines the classical Lagrangian foliation around the full focus-focus leaf. The result applies, for instance, to h-pseudodifferential operators, and to Berezin-Toeplitz operators on prequantizable compact symplectic manifolds.

Article:

Semiclassical inverse spectral theory for singularities of focus-focus type

Journal:

ArXiv preprint

Year:

2013

URL:

http://arxiv.org/abs/1302.2260