Berezin-Toeplitz Quantization over Matrix Domains



Let Ω be a symplectic manifold, with symplectic form ω, and \( \mathcal{H} \) a subspace of L2(Ω, d µ), for some measure µ, admitting a reproducing kernel K. For φC(Ω), the Toeplitz operator T φ with symbol φ is the operator on \( \mathcal{H} \) defined by
$$ {{T}_{\phi }}f=P\left( {\phi f} \right),\:f\in \mathcal{H}, $$
where P: L2((Ω), d µ) → \( \mathcal{H} \) is the orthogonal projection. Using the reproducing kernel K, this can also be written as
$${T_\phi }f(x) = \int_\Omega {d(y)\phi (y)K(x,y)d\mu (y)} .$$


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© Hindustan Book Agency 2007

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsConcordia UniversityMontréalCanada
  2. 2.Mathematics InstitutePrague 1Czech Republic

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