Factorization in a torus and Riemann-Hilbert problems

Details Factorization in a torus and Riemann-Hilbert problems Factorization in a torus and Riemann-Hilbert problems

2010-10-26

arxiv.org/abs/1010.5460v2

Mathematics

Complex Variables

accepted for publication in Journal of Mathematical Analysis and Applications

Scientific paper

A new concept of meromorphic $\Sigma$-factorization, for H\"{o}lder continuous functions defined on a contour $\Gamma$ that is the pullback of $\dot{\mathbb{R}}$ (or the unit circle) in a Riemann surface $\Sigma$ of genus 1, is introduced and studied, and its relations with holomorphic $\Sigma$-factorization are discussed. It is applied to study and solve some scalar Riemann-Hilbert problems in $\Sigma$ and vectorial Riemann-Hilbert problems in $\mathbb{C}$, including Wiener-Hopf matrix factorization, as well as to study some properties of a class of Toeplitz operators with $2 \times 2$ matrix symbols.

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