On the spectrum of the operator which is a composition of integration and substitution

TL;DR

This paper investigates the spectral properties of a Volterra composition operator, which involves integration and substitution, within the space of square-integrable functions on the interval [0,1].

Contribution

It provides a detailed analysis of the spectrum of the Volterra composition operator, a topic not extensively explored before.

Findings

Characterization of the spectrum of the operator.

Identification of spectral types and their properties.

Insights into the operator's behavior in $L_2[0,1]$.

Abstract

We study the spectrum of the Volterra composition operator in the space $L_2[0,1]$