Factorization in a torus and Riemann-Hilbert problems

2010/10/26 by M. C. Câmara, Câmara, M. C., M. T. Malheiro +1
Mathematics · Physics and Astronomy · #30E25 #30F99 #37J35 #47A68 #47B35 #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #math-ph #math.CV #math.FA #math.MP #msc:30E25 #msc:30F99 #msc:37J35 #msc:47A68 #msc:47B35

paper · pdf · doi:10.48550/arxiv.1010.5460

accepted for publication in Journal of Mathematical Analysis and Applications

arxiv created 2011/08/02 · arxiv updated 2011/08/03

Abstract

A new concept of meromorphic Σ-factorization, for Hölder continuous functions defined on a contour Γ that is the pullback of ℝ (or the unit circle) in a Riemann surface Σ of genus 1, is introduced and studied, and its relations with holomorphic Σ-factorization are discussed. It is applied to study and solve some scalar Riemann-Hilbert problems in Σ and vectorial Riemann-Hilbert problems in ℂ, including Wiener-Hopf matrix factorization, as well as to study some properties of a class of Toeplitz operators with 2 × 2 matrix symbols.

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