The Wiener--Hopf Technique, its Generalisations 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 are presented, approximation methods are outlined and the main areas of applications are mentioned. The aim of the paper is to sketched some perspective of the development of this method, importance of bringing together pure and applied analysis to most effectively use of the Wiener--Hopf technique.

References in corpus (14)

• Aerodynamic noise from rigid trailing edges with finite porous extensions
• Analytical methods for perfect wedge diffraction: a review
• Evaluation of the Lazarus-Leblond constants in the asymptotic model of the interfacial wavy crack
• Hall and dissipative viscosity effects on edge magnetoplasmons
• An asymptotic method of factorization of a class of matrix-functions
• Diffraction by a quarter-plane. Analytical continuation of spectral functions
• Factorization of piecewise constant matrix functions and systems of linear differential equations
• Scattering by two staggered semi-infinite cracks on square lattice: an application of asymptotic Wiener-Hopf factorization
• Sommerfeld--type integrals for discrete diffraction problems
• Continuum limit of discrete Sommerfeld problems on square lattice
• Edge plasmon-polaritons on isotropic semi-infinite conducting sheets
• Peristalsis by pulses of activity
• Wiener-Hopf matrix factorization using ordinary differential equations in the commutative case
• Criteria for commutative factorization of a class of algebraic matrices