On Toeplitz localization operators
Ondrej Hutn\'ik, M\'aria Hutn\'ikov\'a
TL;DR
This paper introduces a unified framework for analyzing Toeplitz localization operators using Calderón and Gabor reproducing formulas, revealing their connection to pseudodifferential operators with specific symbols.
Contribution
It provides a novel unified approach to study Toeplitz localization operators, linking them to pseudodifferential operators via reproducing formulas.
Findings
Operators can be viewed as pseudodifferential operators with line or compound symbols.
Unified approach simplifies analysis of Toeplitz localization operators.
Potential applications in signal processing and harmonic analysis.
Abstract
We present a unified approach to study properties of Toeplitz localization operators based on the Calder\'on and Gabor reproducing formula. We show that these operators with functional symbols on a plane domain may be viewed as certain pseudodifferential operators (with symbols on a line, or certain compound symbols).
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