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arXiv · 1302.2260

Semiclassical inverse spectral theory for singularities of focus-focus type

Álvaro Pelayo·San Vũ Ngoc
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Abstract

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.

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Álvaro Pelayo, San Vũ Ngoc. 2013-02-09. Semiclassical inverse spectral theory for singularities of focus-focus type. https://doi.org/10.1007/s00220-014-1998-9

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