Bounded Berezin-Toeplitz operators on the Segal-Bargmann space

Details Bounded Berezin-Toeplitz operators on the Segal-Bargmann space Bounded Berezin-Toeplitz operators on the Segal-Bargmann space

2008-06-02

arxiv.org/abs/0806.0193v3

Mathematics

Functional Analysis

13 pages, no figure, a few minor changes, final version

Scientific paper

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 Sj\"ostrand. 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 Sj\"ostrand. Our method of proofs is based on the pseudodifferential calculus and the heat flow determined by the phase function of the Bargmann transform.

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