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

Yamane, Hideshi

doi:10.1090/proc/14398

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

Proc. Amer. Math. Soc. 147 (2019), 2147-2157

DOI: https://doi.org/10.1090/proc/14398

Published electronically: January 18, 2019

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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 Schrödinger equations.

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