Factorization of a class of symbols with outer functions |
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Authors: | Antó nio F. dos Santos,Pedro F. dos Santos |
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Affiliation: | Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Portugal |
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Abstract: | In this paper the Wiener–Hopf (or Riemann–Hilbert) factorization of a class of symbols important in applications is studied. The symbols in this class involve outer functions that appear in applications such as diffraction by strip gratings and infinite-dimensional integrable systems. The method proposed is based on the reduction of a vector Riemann–Hilbert to a scalar problem on an appropriate Riemann surface. Two examples are given leading to the Riemann sphere and to an elliptic curve. |
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Keywords: | Factorization Riemann&ndash Hilbert problems Riemann surfaces |
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