Reinvigorating the Wiener-Hopf technique in the pursuit of understanding processes and materials

David Abrahams, Xun Huang, Anastasia V. Kisil, Gennady Mishuris, Michael Nieves, Sergei Rogosin, Ilya M. Spitkovsky

Abstract

The Wiener-Hopf (WH) method was created in 1931, by Norbert Wiener and Eberhard Hopf, to deliver exact solutions to integral equations with convolution-type kernels on a half-line. It appears that this problem is closely related to that posed by Riemann in 1857 on the problem concerning the construction of a Fuchsian system of differential equations with given singular points and a prescribed monodromy group. This later became known as the 21st Hilbert problem. The WH method is a powerful and long-standing tool that served as a catalyst in broadening the applicability of Fourier analysis, owing to the essential characteristics of analytic functions.

Locations

• National Science Review - View - PDF
• PubMed Central - View
• Aberystwyth Research portal (Aberystwyth University) - View - PDF
• PubMed - View