Open AccessThe Wiener–Hopf technique, its generalizations and applications: constructive and approximate methods
Author(s) -
Anastasia V. Kisil,
I. David Abrahams,
Gennady Mishuris,
Sergei Rogosin
Publication year - 2021
Publication title -
proceedings - royal society. mathematical, physical and engineering sciences
Language(s) - English
Resource type - Journals
eISSN - 1471-2946
pISSN - 1364-5021
DOI - 10.1098/rspa.2021.0533
Subject(s) - constructive , factorization , mathematics , algebra over a field , matrix (chemical analysis) , mathematical optimization , calculus (dental) , computer science , pure mathematics , algorithm , process (computing) , operating system , medicine , materials science , dentistry , composite material
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.