Factorization in a torus and Riemann-Hilbert problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:386

Article

Camara, M. C.¹  Malheiro, M. T.² 

[1] Univ Tecn Lisboa, Dep Matemat, Inst Super Tecn, P-1049001 Lisbon, Portugal

[2] Univ Minho, Ctr Matemat, Dept Matemat & Aplicacoes, P-4800058 Guimaraes, Portugal

关键词: Riemann-Hilbert problems;    Factorization;    Riemann surfaces;    Toeplitz operators;   

DOI  :  10.1016/j.jmaa.2011.08.002

来源: Elsevier

【 摘 要 】

A new concept of meromorphic Sigma-factorization, for Holder continuous functions defined on a contour Gamma that is the pullback of R(over dot) (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 C, including Wiener-Hopf matrix factorization, as well as to study some properties of a class of Toeplitz operators with 2 x 2 matrix symbols. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free