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TW 401
Adhemar Bultheel, Pablo González-Vera, Erik Hendriksen, Olav Njåstad
Orthogonal rational functions on the unit circle: from the scalar to the matrix case
Abstract
The purpose of these lecture notes is to give a short introduction to the theory of orthogonal rational functions (ORF) on the unit circle. We start with the classical problem of linear prediction of a stochastic process to give a motivation for the study of Szeg\H{o}'s problem and to show that in this context it will turn out that not as much the ORF but rather the reproducing kernels will play a central role. Another example of rational Krylov iteration shows that it might also be interesting to consider ORF on the real line, which we shall not discuss in these lectures.
In a second part we will show that most of the results of the scalar case thanslate easily to the case of matrix valued orthogonal rational functions (MORF).
report.pdf (373K) / mailto: A. Bultheel