Colloquium September 26
Date: Friday September 26
Time: 16:00 to 17:00
Place: 455 McBryde, Commons Room
Speaker: Gilbert Groenewald of the Math Dept
Title: Distribution of zeros of continuous analogues of orthogonal matrix polynomials
Abstract
Orthogonal polynomials arise naturally in connection
with moment problems and best approximation problems in a
weighted L^2-norm. A classical theorem of Szego states that the
zeros of the polynomials orthogonal with respect to a positive
weight on the unit circle all lie inside the unit circle. Work
of Krein extends the result to matrix polynomials orthogonal
with respect to a matrix weight on the unit circle orthogonal
with respect to an indefinite matrix weight. Continuous
analogues of these results were obtained by Krein-Langer for
the scalar case. We discuss recent work on the continuous
analogues of the general matrix-valued case. A novel feature
of our approach to these types of results is the application
of the state-space method from linear systems theory.
This is a report on joint work with M.A. Kaashoek (Free
University of Amsterdam).
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