Complex symmetric weighted Composition Differentiation Operators

TL;DR

This paper characterizes complex symmetric weighted composition differentiation operators on the Hardy space $H^2$, explores their normal and self-adjoint properties, and extends prior research in this area.

Contribution

It provides a complete characterization of complex symmetric weighted composition differentiation operators on $H^2$, including conditions for normality and self-adjointness.

Findings

Characterization of complex symmetric weighted composition differentiation operators

Conditions for normality and self-adjointness on $H^2$

Extension of previous work by Fatehi and Hammond

Abstract

In this note, we completely characterize complex symmetric weighted composition differentiation operator on the Hardy space $H^2$ with respect to the conjugation operator $C_{\lambda,\alpha}$. Meanwhile, the normal and self-adjoint of the weighted composition differentiation operators on the Hardy space $H^2$ are also studied. This note could be considered as a continuation of the work initiated by Fatehi and Hammond.