Bounded Berezin-Toeplitz operators on the Segal-Bargmann space
Functional Analysis
2009-01-23 v3
Abstract
We discuss the boundedness of Berezin-Toeplitz operators on a generalized Segal-Bargmann space (Fock space) over the complex -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.
Cite
@article{arxiv.0806.0193,
title = {Bounded Berezin-Toeplitz operators on the Segal-Bargmann space},
author = {Hiroyuki Chihara},
journal= {arXiv preprint arXiv:0806.0193},
year = {2009}
}
Comments
13 pages, no figure, a few minor changes, final version