Factorization in a torus and Riemann–Hilbert problems
Copyright policy )Factorization in a torus and Riemann–Hilbert problems
A new concept of meromorphic $Σ$-factorization, for Hölder continuous functions defined on a contour $Γ$ that is the pullback of $\dot{\mathbb{R}}$ (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 $\mathbb{C}$, including Wiener-Hopf matrix factorization, as well as to study some properties of a class of Toeplitz operators with $2 \times 2$ matrix symbols.
accepted for publication in Journal of Mathematical Analysis and Applications
- University of Lisbon Portugal
- UNIVERSIDADE TECNICA DE LISBOA - UTL Portugal
- Centro de Matemática Portugal
- Centro de Matemática Portugal
- Technical University of Lisbon Portugal
Riemann-Hilbert problem, Riemann–Hilbert problems, Mathematics - Complex Variables, Applied Mathematics, Riemann-Hilbert problems, FOS: Physical sciences, torus, Mathematical Physics (math-ph), Functional Analysis (math.FA), Mathematics - Functional Analysis, Riemann surfaces, Toeplitz operator, Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators, Toeplitz operators, Hankel operators, Wiener-Hopf operators, FOS: Mathematics, Boundary value problems in the complex plane, Riemann-Hilbert problems in context of PDEs, Factorization, Complex Variables (math.CV), 47A68, 30E25, 30F99, 47B35, 37J35, Toeplitz operators, Analysis, Mathematical Physics
Riemann-Hilbert problem, Riemann–Hilbert problems, Mathematics - Complex Variables, Applied Mathematics, Riemann-Hilbert problems, FOS: Physical sciences, torus, Mathematical Physics (math-ph), Functional Analysis (math.FA), Mathematics - Functional Analysis, Riemann surfaces, Toeplitz operator, Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators, Toeplitz operators, Hankel operators, Wiener-Hopf operators, FOS: Mathematics, Boundary value problems in the complex plane, Riemann-Hilbert problems in context of PDEs, Factorization, Complex Variables (math.CV), 47A68, 30E25, 30F99, 47B35, 37J35, Toeplitz operators, Analysis, Mathematical Physics
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