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arXiv · 1009.5123

Symbols of truncated Toeplitz operators

Anton Baranov·Roman Bessonov·Vladimir Kapustin
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Abstract

We consider three problems connected with coinvariant subspaces of the backward shift operator in Hardy spaces $H^p$: 1) properties of truncated Toeplitz operators; 2) Carleson-type embedding theorems for the coinvariant subspaces; 3) factorizations of pseudocontinuable functions from $H^1$. These problems turn out to be closely connected and even, in a sense, equivalent. The new approach based on the factorizations allows us to answer a number of challenging questions about truncated Toeplitz operators posed by Donald Sarason.

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Anton Baranov, Roman Bessonov, Vladimir Kapustin. 2010-09-26. Symbols of truncated Toeplitz operators. https://doi.org/10.1016/j.jfa.2011.08.005

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