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A product expansion for Toeplitz operators on the Fock space


Author: Raffael Hagger
Journal: Proc. Amer. Math. Soc. 147 (2019), 4823-4833
MSC (2010): Primary 47B35; Secondary 46L65, 30H20
DOI: https://doi.org/10.1090/proc/14661
Published electronically: June 10, 2019
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Abstract: We study the asymptotic expansion of the product of two Toeplitz operators on the Fock space. In comparison to earlier results we require significantly fewer derivatives and get the expansion to arbitrary order. This, in particular, improves a result of Borthwick related to Toeplitz quantization. In addition, we derive an intertwining identity between the Berezin star product and the sharp product.


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Additional Information

Raffael Hagger
Affiliation: Institut für Analysis, Leibniz Universität Hanover, 30167 Hannover, Germany
Email: raffael.hagger@math.uni-hannover.de

DOI: https://doi.org/10.1090/proc/14661
Received by editor(s): August 30, 2018
Received by editor(s) in revised form: February 8, 2019
Published electronically: June 10, 2019
Communicated by: Stephan Ramon Garcia
Article copyright: © Copyright 2019 American Mathematical Society