The Wiener-Hopf technique, its generalizations and applications: constructive and approximate methods

Anastasia V Kisil; I David Abrahams; Gennady Mishuris; Sergei V Rogosin

doi:10.1098/rspa.2021.0533

The Wiener-Hopf technique, its generalizations and applications: constructive and approximate methods

Proc Math Phys Eng Sci. 2021 Oct;477(2254):20210533. doi: 10.1098/rspa.2021.0533. Epub 2021 Oct 20.

Authors

Anastasia V Kisil¹, I David Abrahams², Gennady Mishuris³, Sergei V Rogosin⁴

Affiliations

¹ Department of Mathematics, University of Manchester, Manchester M13 9PL, UK.
² Isaac Newton Institute for Mathematical Sciences, University of Cambridge, Cambridge CB3 0EH, UK.
³ Aberystwyth University, Penglais, Aberystwyth SY23 3BZ, UK.
⁴ Belarusian State University, Nezavisimosti Avenue, 4, Minsk 220030, Belarus.

Abstract

This paper reviews the modern state of the Wiener-Hopf factorization method and its generalizations. The main constructive results for matrix Wiener-Hopf problems are presented, approximate methods are outlined and the main areas of applications are mentioned. The aim of the paper is to offer an overview of the development of this method, and demonstrate the importance of bringing together pure and applied analysis to effectively employ the Wiener-Hopf technique.

Keywords: Riemann boundary value problem; Riemann–Hilbert; Wiener–Hopf; applications; factorization; partial indices.

Publication types

Review