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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Wiener-Hopf factorisation through an intermediate space and applications to diffraction theory

## Wiener-Hopf factorisation through an intermediate space and applications to diffraction theoryAdd to your list(s) Download to your calendar using vCal - Frank Speck (Universidade de Lisboa)
- Monday 12 August 2019, 10:00-11:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact INI IT. WHTW01 - Factorisation of matrix functions: New techniques and applications An operator factorisation conception is investigated for a general Wiener-Hopf operator $W = P_2 A | ^{p$ spaces and various other factorisation approaches. As applications we consider interface problems in weak formulation for the n-dimensional Helmholtz equation in $\Omega = \mathbb{R}}n^{n_-$ (due to $x_n > 0$ or $x_n < 0$, respectively), where the interface $\Gamma = \partial \Omega$ is identified with $\mathbb{R}}{n-1}$ and divided into two parts, $\Sigma$ and $\Sigma'$, with different transmission conditions of first and second kind. These two parts are half-spaces of $\mathbb{R}^{$ (half-planes for $n = 3$). We construct explicitly resolvent operators acting from the interface data into the energy space $H}1(\Omega)$. The approach is based upon the present factorisation conception and avoids an interpretation of the factors as unbounded operators. In a natural way, we meet anisotropic Sobolev spaces which reflect the edge asymptotic of diffracted waves.This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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