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Bounded Berezin-Toeplitz operators on the Segal-Bargmann space

2008/06/02 by Hiroyuki Chihara, Chihara, Hiroyuki
Mathematics · #47B32 #47B35 #47G30 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #math.FA #msc:47B32 #msc:47B35 #msc:47G30

paper · pdf · doi:10.48550/arxiv.0806.0193

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

openalex publication_date 2008/06/02 · arxiv created 2009/01/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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