Vol. 1, No. 3, 2019

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Positivity, complex FIOs, and Toeplitz operators

Lewis A. Coburn, Michael Hitrik and Johannes Sjöstrand

Vol. 1 (2019), No. 3, 327–357
Abstract

We establish a characterization of complex linear canonical transformations that are positive with respect to a pair of strictly plurisubharmonic quadratic weights. As an application, we show that the boundedness of a class of Toeplitz operators on the Bargmann space is implied by the boundedness of their Weyl symbols.

Keywords
positive Lagrangian plane, positive canonical transformation, strictly plurisubharmonic quadratic form, Fourier integral operator in the complex domain, Toeplitz operator
Mathematical Subject Classification 2010
Primary: 32U05, 32W25, 35S30, 47B35, 70H15
Milestones
Received: 3 July 2018
Revised: 26 February 2019
Accepted: 4 May 2019
Published: 17 July 2019
Authors
Lewis A. Coburn
Department of Mathematics
SUNY at Buffalo
Buffalo, NY
United States
Michael Hitrik
Department of Mathematics
University of California
Los Angeles, CA
United States
Johannes Sjöstrand
IMB
Université de Bourgogne
Dijon
France