Bounded Berezin-Toeplitz Operators on the Segal-Bargmann Space

摘要

We discuss the boundedness of Berezin-Toeplitz operators on a gen_eralized Segal-Bargmann space (Fock space) over the complex n-space. This space is characterized by the image of a global Bargmann-type transform in_troduced by Sj_strand. We also obtain the deformation estimates of the com_position of Berezin-Toeplitz operators whose symbols and their derivatives up to order three are in the Wiener algebra of Sj_strand. Our method of proofs is based on the pseudodifferential calculus and the heat flow determined by the phase function of the Bargmann transform.