Communications in Mathematical Physics

, Volume 329, Issue 2, pp 809–820 | Cite as

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 singular value of a quantum integrable system determines the classical Lagrangian foliation around the full focus–focus leaf. The result applies, for instance, to ħ-pseudodifferential operators on cotangent bundles and Berezin–Toeplitz operators on prequantizable compact symplectic manifolds.


Integrable System Toeplitz Operator Cotangent Bundle Principal Symbol Inverse Spectral Problem 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  2. 2.Mathematics DepartmentWashington University in St. LouisSt. LouisUSA
  3. 3.Institut Universitaire de FranceParisFrance
  4. 4.Institut de Recherches Mathématiques de RennesUniversité de Rennes 1Rennes CedexFrance

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