Complex FIOs and composition of Toeplitz operators
Lewis Coburn, Michael Hitrik, Johannes Sjoestrand
TL;DR
This paper investigates Toeplitz operators with exponential quadratic symbols on the Bargmann space, analyzing their composition through the lens of complex Fourier integral operators to establish conditions for their product to remain Toeplitz.
Contribution
It introduces a novel approach by applying complex Fourier integral operator theory to characterize the composition of specific Toeplitz operators.
Findings
Derived sufficient conditions for the composition to be a Toeplitz operator
Extended the understanding of Toeplitz operator algebra in the complex domain
Linked Toeplitz operator composition to Fourier integral operator theory
Abstract
We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of complex quadratic forms, from the point of view of Fourier integral operators in the complex domain. Sufficient conditions are established for the composition of two such operators to be a Toeplitz operator.
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Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic and Geometric Analysis · Advanced Algebra and Geometry