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Wiener-Hopf factorisation on the unit circle: some examples of discrete scattering problems

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WHTW01 - Factorisation of matrix functions: New techniques and applications

I will provide certain examples of scattering problems, motivated by lattice waves (phonons), electronic waves under certain assumptions, nanoscale effects, etc in crystals. The mathematical formulation is posed on lattices and involves difference equations that can be reduced to the problem of Wiener-Hopf on the unit circle (in an annulus in complex plane). In some of these examples, the Wiener-Hopf  problem is scalar, while in other cases it is a matrix Wiener-Hopf problem. For the latter, in a few cases it may be reduced to a scalar problem but it appears to be not the case in others. Some of these problems can be considered as discrete analogues of well-known Wiener-Hopf equations in continuum models on the real line (in an strip in complex plane), a few of which are still open problems.

This talk is part of the Isaac Newton Institute Seminar Series series.

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