A Riemann-Hilbert Approach to H∞-Optimization

Professor Elias Wegert (Freiberg, visiting Isaac Newton Institute, Cambridge). Part of the Analysis and Applications Seminar Series.

Though Bernhard Riemann's thesis is commonly known as the source of the celebrated Riemann mapping theorem, Riemann himself considered conformal mapping just as an example to illustrate his ideas about a more general class of nonlinear boundary value problems for analytic functions. The talk is intended as an introduction to these Riemann-Hilbert problems.

In the first part we address the existence and uniqueness of solutions for different problem classes. In the second part, a connection between Riemann-Hilbert problems and a class of extremal problems is established. Solutions to Riemann-Hilbert problems are characterized by an extremal principle which generalizes the classical maximum principle and Schwarz' lemma. In the end we present an application to the design of dynamical systems.

 
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Be Curious 2020