A characterization for complex symmetric Toeplitz operators

TL;DR

This paper characterizes complex symmetric Toeplitz operators on the Hardy space using an orthonormal basis of rational functions, providing examples with non-trigonometric symbols, thus expanding understanding of their structure.

Contribution

It introduces a new characterization of complex symmetric Toeplitz operators on Hardy spaces using rational function bases, including novel examples with non-trigonometric symbols.

Findings

Characterization of complex symmetric Toeplitz operators using rational basis

Examples of such operators with non-trigonometric symbols

Enhanced understanding of the structure of these operators

Abstract

In this paper we use orthonormal basis for the Hardy space $H^{2}(\mathbb{T})$, formed by rational functions, to characterize complex symmetric Toeplitz operators on $H^{2}(\mathbb{T})$. As a result, we get examples of these operators whose symbols are non-trigonometric functions.