<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we introduce the use of a powerful tool from theoretical complex analysis, the Blaschke product, for the solution of Riemann-Hilbert problems. Classically, Riemann-Hilbert problems are considered for analytic functions. We give a factorization theorem for meromorphic functions over simply connected nonempty proper open subsets of the complex plane and use this theorem to solve Riemann-Hilbert problems where the given data consists of a meromorphic function.</p></abstract>

In this paper, we introduce the use of a powerful tool from theoretical complex analysis, the Blaschke product, for the solution of Riemann-Hilbert problems. Classically, Riemann-Hilbert problems are considered for analytic functions. We give a factorization theorem for meromorphic functions over simply connected nonempty proper open subsets of the complex plane and use this theorem to solve Riemann-Hilbert problems where the given data consists of a meromorphic function.

Solving Riemann-Hilbert problems with meromorphic functions

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Solving Riemann-Hilbert problems with meromorphic functions"}

In this paper, we introduce the use of a powerful tool from theoretical complex analysis, the Blaschke product, for the solution of Riemann-Hilbert problems....

Solving Riemann-Hilbert problems with meromorphic functions

Published Online: Aug 17, 2019

Page range: 117 - 130

Received: Apr 05, 2018

DOI: https://doi.org/10.2478/ausm-2019-0010

Keywords
Riemann-Hilbert problems, meromorphic functions, positive definite functions

© 2019 Dan Kucerovsky et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Solving Riemann-Hilbert problems with meromorphic functions

Published Online: Aug 17, 2019

Page range: 117 - 130

Received: Apr 05, 2018

DOI: https://doi.org/10.2478/ausm-2019-0010

KeywordsRiemann-Hilbert problems, meromorphic functions, positive definite functions

© 2019 Dan Kucerovsky et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Riemann-Hilbert problems, meromorphic functions, positive definite functions