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TitleFactorization in a torus and Riemann-Hilbert problems
Author(s)Câmara, M. C.
Malheiro, Teresa
KeywordsRiemann-Hilbert problem
Riemann surfaces
Toeplitz operator
Riemann-Hilbert problems
Toeplitz operators
Issue date2012
JournalJournal of Mathematical Analysis and Applications
Abstract(s)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.
DescriptionArticle in press, corrected proof
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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