Range Spaces of Co-analytic Toeplitz Operators

TL;DR

This paper investigates the properties of range spaces of co-analytic Toeplitz operators, emphasizing boundary behavior and orthogonal decompositions to deepen understanding of their functional structure.

Contribution

It introduces a detailed analysis of the boundary behavior and orthogonal decompositions of the range spaces of co-analytic Toeplitz operators, offering new insights into their structure.

Findings

Characterization of boundary behavior of functions in the range spaces

Development of an orthogonal decomposition framework for these spaces

Enhanced understanding of the functional structure of co-analytic Toeplitz operator ranges

Abstract

We discuss the range spaces of Toeplitz operators with co-analytic symbols where we focus on the boundary behavior of the functions in these spaces as well as a natural orthogonal decomposition of this range.