Journal of Geometric Analysis

, Volume 18, Issue 2, pp 565–611 | Cite as

Toeplitz Operators on Symplectic Manifolds

  • Xiaonan Ma
  • George Marinescu


We study the Berezin-Toeplitz quantization on symplectic manifolds making use of the full off-diagonal asymptotic expansion of the Bergman kernel. We give also a characterization of Toeplitz operators in terms of their asymptotic expansion. The semi-classical limit properties of the Berezin-Toeplitz quantization for non-compact manifolds and orbifolds are also established.


Toeplitz operator Berezin-Toeplitz quantization Bergman kernel spinc Dirac operator 

Mathematics Subject Classification (2000)

58F06 81S10 32A25 47B35 


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Authors and Affiliations

  1. 1.UFR de MathématiquesUniversité Denis Diderot—Paris 7Paris Cedex 13France
  2. 2.Mathematisches InstitutUniversität zu KölnKölnGermany
  3. 3.Institute of Mathematics ‘Simion Stoilow’Romanian AcademyBucharestRomania

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