Mathematical Research Letters

Volume 28 (2021)

Number 3

Weyl symbols and boundedness of Toeplitz operators

Pages: 681 – 696

DOI: https://dx.doi.org/10.4310/MRL.2021.v28.n3.a3

Authors

Lewis Coburn (Department of Mathematics, State University of New York, Buffalo, N.Y., U.S.A.)

Michael Hitrik (Department of Mathematics, University of California, Los Angeles, Cal., U.S.A.)

Johannes Sjöstrand (IMB, Université de Bourgogne, Dijon, France)

Francis White (Department of Mathematics, University of California, Los Angeles, Cal., U.S.A.)

Abstract

We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding Weyl symbols.

Received 13 July 2019

Accepted 20 March 2020

Published 2 June 2021