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Positivity, complex FIOs,
and Toeplitz operators
Lewis A. Coburn, Michael Hitrik and Johannes Sjöstrand |
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Vol. 1 (2019), No. 3, 327–357
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Abstract |
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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. |
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Keywords
positive Lagrangian plane, positive canonical
transformation, strictly plurisubharmonic quadratic form,
Fourier integral operator in the complex domain, Toeplitz
operator
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Mathematical Subject Classification 2010
Primary: 32U05, 32W25, 35S30, 47B35, 70H15
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Milestones
Received: 3 July 2018
Revised: 26 February 2019
Accepted: 4 May 2019
Published: 17 July 2019
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Authors |
| Lewis A. Coburn | |
| Department of Mathematics SUNY at Buffalo Buffalo, NY United States |
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| Michael Hitrik | |
| Department of Mathematics University of California Los Angeles, CA United States |
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| Johannes Sjöstrand | |
| IMB Université de Bourgogne Dijon France |
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