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arXiv · 1805.12366

Riemann-Hilbert factorization of matrices invariant under inversion in a circle

Hideshi Yamane
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Abstract

We consider matrix functions with certain invariance under inversion in the unit circle. If such a function satisfies a positivity assumption on the unit circle, then only zero partial indices appear in its Riemann-Hilbert (Wiener-Hopf) factorization. It implies the unique solvability of a certain class of Riemann-Hilbert boundary value problems. It includes the ones associated with the inverse scattering transform of the focusing/defocusing integrable discrete nonlinear Schr\"odinger equations.

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Hideshi Yamane. 2018-05-31. Riemann-Hilbert factorization of matrices invariant under inversion in a circle. https://arxiv.org/abs/1805.12366

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