Bounded Berezin-Toeplitz Operators on the Segal-Bargmann Space
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We discuss the boundedness of Berezin-Toeplitz operators on a generalized Segal-Bargmann space (Fock space) over the complex n-space. This space is characterized by the image of a global Bargmann-type transform introduced by Sjöstrand. We also obtain the deformation estimates of the composition of Berezin-Toeplitz operators whose symbols and their derivatives up to order three are in the Wiener algebra of Sjöstrand. Our method of proofs is based on the pseudodifferential calculus and the heat flow determined by the phase function of the Bargmann transform.
Keywords.Bargmann transform Segal-Bargmann space Berezin-Toeplitz operator pseudodifferential operator
Mathematics Subject Classification (2000).Primary 47B35 Secondary 47B32, 47G30
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