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Complex Approximations, Orthogonal Polynomials and Applications (CAOPA)
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An orthogonal polynomials approach to Poncelet’s theorem, numerical range, Blaschke products, and beyond… A. Martínez-Finkelshtein Baylor University |
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Abstract: For several decades, the relationship between Blaschke products, Poncelet’s Theorem, and numerical range of completely non-unitary contractions has been the focus of extensive research. Our goal is to discuss a connection between these topics and the theory of orthogonal polynomials on the unit circle. This recently discovered approach allows to prove several new results, to interpret the existing theory in a new context, and also to understand further connections with other areas of geometry and analysis. This is a joint work with Brian Simanek and Barry Simon. |