Algebras of Hausdorff Operators on the Real Line

TL;DR

This paper develops a symbol calculus for one-dimensional Hausdorff operators on the real line, providing a framework for analyzing these operators in a broad setting.

Contribution

It introduces a comprehensive symbol calculus for Hausdorff operators on L^2(R), extending previous methods to the most general form.

Findings

Established a symbol calculus for Hausdorff operators

Extended analysis to the most general form of these operators

Provided tools for further spectral and functional analysis

Abstract

The aim of this work is to derive a symbol calculus on $L^2(\mathbb{R})$ for one-dimensional Hausdorff operators in apparently the most general form.