Wiener algebra for the quaternions

TL;DR

This paper extends the Wiener algebra to quaternionic functions, establishing fundamental theorems and applications to operators, thereby broadening the algebra's scope in mathematical analysis.

Contribution

It introduces a quaternionic Wiener algebra, proves a Wiener-Lévy theorem and factorization results, and applies these to Toeplitz and Wiener-Hopf operators.

Findings

Established a quaternionic Wiener algebra for discrete and continuous cases.

Proved a Wiener-Lévy type theorem in the quaternionic setting.

Developed applications to Toeplitz and Wiener-Hopf operators.

Abstract

We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-L\'evy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener-Hopf operators.