- Constructive Mathematical Analysis
- Vol: 2 Issue: 4
- From Sommerfeld Diffraction Problems to Operator Factorisation
From Sommerfeld Diffraction Problems to Operator Factorisation
Authors : Frank - Olme Speck
Pages : 183-216
Doi:10.33205/cma.620578
View : 11 | Download : 7
Publication Date : 2019-12-01
Article Type : Research
Abstract :This article presents a brief survey devoted to the interplay between diffraction and operator theory, particularly between the so-called canonical diffraction problems (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