From Sommerfeld Diffraction Problems to Operator Factorisation

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Constructive Mathematical Analysis
Volume:2 Issue:4
From Sommerfeld Diffraction Problems to Operator Factorisation

From Sommerfeld Diffraction Problems to Operator Factorisation

Pages : 183-216

View : 29 | Download : 7

Publication Date : 2019-12-01

Article Type : Research Paper

Abstract :This article presents a brief survey devoted to the interplay between diffraction and operator theory, particularly between the so-called canonical diffraction problems insert ignore into journalissuearticles values(exemplified by Sommerfeld half-plane problems); on one hand and operator factorisation theory on the other hand. It is shown how operator factorisation concepts appear in a natural way from applications and how they can help to find solutions rigorously in case of well-posed problems or how to normalize problems by an adequate change of function spaces.
Keywords : Sommerfeld problem, diffraction, Wiener Hopf method, Wiener Hopf operator, factorisation, intermediate space, generalised inverse, op erator relation

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