@article{1bb580b2dc1641f59df248430498d37f,
title = "The Wiener-Hopf technique, its generalizations and applications: Constructive and approximate methods",
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 = "Wiener-Hopf, Riemann-Hilbert, factorization, partial indices, Riemann boundary value problem, applications, TRIANGULAR-MATRIX-FUNCTIONS, EXPLICIT FACTORIZATION, LINEAR CONJUGATION, PADE APPROXIMANTS, WEIGHT-FUNCTIONS, HALF-SPACE, ASYMPTOTIC FACTORIZATION, 2-DIMENSIONAL MODEL, ACOUSTIC SCATTERING, PLANE-WAVE",
author = "Kisil, {Anastasia V.} and Abrahams, {I. David} and Gennady Mishuris and Rogosin, {Sergei V.}",
note = "Funding Information: The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, for support and hospitality during the programme {\textquoteleft}Bringing pure and applied analysis together via the Wiener–Hopf technique, its generalizations and applications{\textquoteright} where some of the work on this article was undertaken (supported by EPSRC grant no EP/R014604/1). A.V.K. is supported by Royal Society Dorothy Hodgkin Research Fellowship and Dame Kathleen Ollerenshaw Fellowship. S.V.R. is partially supported by the Belarusian Fund for Fundamental Research through grant F20MS-083. G.M. is supported by the Royal Society Wolfson Research Merit Award and Ser Cymru Future Generations Industrial Fellowship. Acknowledgements Publisher Copyright: {\textcopyright} 2021 The Authors.",
year = "2021",
month = oct,
day = "27",
doi = "10.1098/rspa.2021.0533",
language = "English",
volume = "477",
journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",
issn = "1364-5021",
publisher = "Royal Society",
number = "2254",
}