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Commutative Algebras of Toeplitz Operators and Lagrangian Foliations

  • R. Quiroga-Barranco
Part of the Operator Theory: Advances and Applications book series (OT, volume 210)

Abstract

Let D be a homogeneous bounded domain of ℂ n and \( \mathcal{A} \) a set of (anti-Wick) symbols that defines a commutative algebra of Toeplitz operators on every weighted Bergman space of D. We prove that if \( \mathcal{A} \) is rich enough, then it has an underlying geometric structure given by a Lagrangian foliation.

Mathematics Subject Classification (2000)

47B35 32M10 57R30 53D05 

Keywords

Toeplitz operators Lagrangian submanifolds foliations 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • R. Quiroga-Barranco
    • 1
  1. 1.Centro de Investigación en MatemáticasGuanajuatoMéxico

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