POSITIVITY, COMPLEX FIOS, AND TOEPLITZ OPERATORS

Lewis A. Coburn; Michael Hitrik; Johannes Sjöstrand

doi:10.2140/paa.2019.1.327

POSITIVITY, COMPLEX FIOS, AND TOEPLITZ OPERATORS

Lewis A. Coburn
, Michael Hitrik
, Johannes Sjöstrand

Mathematics

University of California at Los Angeles
Université de Bourgogne

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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.

Original language	English
Pages (from-to)	327-357
Number of pages	31
Journal	Pure and Applied Analysis
Volume	1
Issue number	3
DOIs	https://doi.org/10.2140/paa.2019.1.327
State	Published - 2019

Keywords

Fourier integral operator in the complex domain
positive canonical transformation
positive Lagrangian plane
strictly plurisubharmonic quadratic form
Toeplitz operator

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10.2140/paa.2019.1.327

Cite this

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title = "POSITIVITY, COMPLEX FIOS, AND TOEPLITZ OPERATORS",

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 = "Fourier integral operator in the complex domain, positive canonical transformation, positive Lagrangian plane, strictly plurisubharmonic quadratic form, Toeplitz operator",

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T1 - POSITIVITY, COMPLEX FIOS, AND TOEPLITZ OPERATORS

AU - Coburn, Lewis A.

AU - Hitrik, Michael

AU - Sjöstrand, Johannes

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Fourier integral operator in the complex domain

KW - positive canonical transformation

KW - positive Lagrangian plane

KW - strictly plurisubharmonic quadratic form

KW - Toeplitz operator

UR - https://www.scopus.com/pages/publications/85096812104

U2 - 10.2140/paa.2019.1.327

DO - 10.2140/paa.2019.1.327

M3 - Article

AN - SCOPUS:85096812104

SN - 2578-5893

VL - 1

SP - 327

EP - 357

JO - Pure and Applied Analysis

JF - Pure and Applied Analysis

IS - 3

ER -

POSITIVITY, COMPLEX FIOS, AND TOEPLITZ OPERATORS

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Keywords

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