The relationship between a strip Wiener--Hopf problem and a line Riemann--Hilbert problem

TL;DR

This paper unifies the Wiener--Hopf and Riemann--Hilbert factorisation problems, revealing their exact relationship and showing how Wiener--Hopf solutions can be derived from Riemann--Hilbert factorisation under certain conditions.

Contribution

It establishes a precise connection between Wiener--Hopf and Riemann--Hilbert problems, providing a unified framework and methods to derive solutions across both.

Findings

Wiener--Hopf factorisation can be obtained via Riemann--Hilbert factorisation.

The paper clarifies the regularity assumptions needed for each problem.

A unified approach links the two types of factorisation.

Abstract

In this paper the Wiener--Hopf factorisation problem is presented in a unified framework with the Riemann--Hilbert factorisation. This allows to establish the exact relationship between the two types of factorisation. In particular, in the Wiener--Hopf problem one assumes more regularity than for the Riemann--Hilbert problem. It is shown that Wiener--Hopf factorisation can be obtained using Riemann--Hilbert factorisation on certain lines.