Truncated Toeplitz operators and boundary values in nearly invariant subspaces

TL;DR

This paper investigates the boundary behavior of functions in nearly invariant subspaces of the Hardy space and explores the properties of truncated Toeplitz operators acting on these subspaces.

Contribution

It provides new insights into the boundary values of functions in nearly invariant subspaces and analyzes truncated Toeplitz operators within this context.

Findings

Characterization of boundary behavior of functions in nearly invariant subspaces

Analysis of truncated Toeplitz operators on these subspaces

New results on boundary value properties

Abstract

We consider truncated Toeplitz operator on nearly invariant subspaces of the Hardy space $H^2$. Of some importance in this context is the boundary behavior of the functions in these spaces which we will discuss in some detail.