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

Anastasia V. Kisil^*
, I. David Abrahams
, Gennady Mishuris
, Sergei V. Rogosin

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Review Article › peer-review

39 Citations (Scopus)

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.

Original language	English
Article number	20210533
Number of pages	32
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	477
Issue number	2254
Early online date	20 Oct 2021
DOIs	https://doi.org/10.1098/rspa.2021.0533
Publication status	Published - 27 Oct 2021

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

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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.",

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author = "Kisil, \{Anastasia V.\} and Abrahams, \{I. David\} and Gennady Mishuris and Rogosin, \{Sergei V.\}",

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language = "English",

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The Wiener-Hopf technique, its generalizations and applications: Constructive and approximate methods. / Kisil, Anastasia V.; Abrahams, I. David; Mishuris, Gennady et al.
In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 477, No. 2254, 20210533, 27.10.2021.

Research output: Contribution to journal › Review Article › peer-review

TY - JOUR

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T2 - Constructive and approximate methods

AU - Kisil, Anastasia V.

AU - Abrahams, I. David

AU - Mishuris, Gennady

AU - Rogosin, Sergei V.

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AB - 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.

KW - Wiener-Hopf

KW - Riemann-Hilbert

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KW - partial indices

KW - Riemann boundary value problem

KW - applications

KW - TRIANGULAR-MATRIX-FUNCTIONS

KW - EXPLICIT FACTORIZATION

KW - LINEAR CONJUGATION

KW - PADE APPROXIMANTS

KW - WEIGHT-FUNCTIONS

KW - HALF-SPACE

KW - ASYMPTOTIC FACTORIZATION

KW - 2-DIMENSIONAL MODEL

KW - ACOUSTIC SCATTERING

KW - PLANE-WAVE

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DO - 10.1098/rspa.2021.0533

M3 - Review Article

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AN - SCOPUS:85119627890

SN - 1364-5021

VL - 477

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2254

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ER -

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

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Keywords

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