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Cracking the Matrix: Factorisation of a Class of Wiener–Hopf Kernels

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If you have a question about this talk, please contact Mungo G. Aitken.

Wiener–Hopf matrix equations frequently feature in problems of acoustic scattering and bending of solid structures wherein mixed boundary conditions appear. These equations are solved by way of factorising the matrix kernel. However, no systematic procedures for the factorisation of such matrix kernels exist. Instead, researchers have spent much time and effort looking at special cases. One such example is where the kernel is of Khrapkov–Daniele form; an exact factorisation can then be obtained.

This talk will present a problem of acoustic scattering off a right-angled wedge and formulate the associated Wiener–Hopf matrix equation. It will be shown that the matrix kernel is, after some manipulation, of Khrapkov–Daniele form. We will outline the process of factorising this kernel. If time permits, we may briefly discuss some related problems.

This talk is part of the Waves Group (DAMTP) series.

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