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Semiclassical Inverse Spectral Theory for Singularities of Focus–Focus Type

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, NJ, 08540, USA

    Álvaro Pelayo

  2. Mathematics Department, Washington University in St. Louis, One Brookings Drive, Campus Box 1146, St. Louis, MO, 63130-4899, USA

    Álvaro Pelayo

  3. Institut Universitaire de France, Paris, France

    San Vũ Ngọc

  4. Institut de Recherches Mathématiques de Rennes, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes Cedex, France

    San Vũ Ngọc

Authors
  1. Álvaro Pelayo
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  2. San Vũ Ngọc
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Correspondence to Álvaro Pelayo.

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Communicated by S. Zelditch

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Pelayo, Á., Ngọc, S.V. Semiclassical Inverse Spectral Theory for Singularities of Focus–Focus Type. Commun. Math. Phys. 329, 809–820 (2014). https://doi.org/10.1007/s00220-014-1998-9

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  • DOI: https://doi.org/10.1007/s00220-014-1998-9

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