Riemann-Hilbert factorization of matrices invariant under inversion in a circle
Mathematical Physics
2018-06-01 v1 Complex Variables
Functional Analysis
math.MP
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.
Cite
@article{arxiv.1805.12366,
title = {Riemann-Hilbert factorization of matrices invariant under inversion in a circle},
author = {Hideshi Yamane},
journal= {arXiv preprint arXiv:1805.12366},
year = {2018}
}
Comments
12 pages, 3 figures