Symbols of truncated Toeplitz operators
Anton Baranov, Roman Bessonov, Vladimir Kapustin

TL;DR
This paper explores properties of truncated Toeplitz operators, Carleson embeddings, and factorizations in Hardy spaces, revealing their deep interconnections and addressing longstanding questions in the field.
Contribution
It introduces a new factorization-based approach that links three key problems in Hardy spaces, providing answers to open questions about truncated Toeplitz operators.
Findings
Properties of truncated Toeplitz operators clarified
Carleson-type embedding theorems established
Factorizations of pseudocontinuable functions developed
Abstract
We consider three problems connected with coinvariant subspaces of the backward shift operator in Hardy spaces : 1) properties of truncated Toeplitz operators; 2) Carleson-type embedding theorems for the coinvariant subspaces; 3) factorizations of pseudocontinuable functions from . 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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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Harmonic Analysis Research · Algebraic and Geometric Analysis
