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Hurwitz stable and self-interlacing orthogonal polynomials.

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In this survey talk, we consider a few examples of Hurwitz stable and their dual (the so-called) self-interlacing polynomials and discuss a number of interrelations between theory of orthogonal polynomials, moment theory, and the root distributions of polynomials. Some specific relations between the Jacobi polynomials and certain  Hurwitz stable polynomials will be presented and an answer to a question of Geno Nikolov on interlacing properties of the Jacobi polynomials will be provided. We will also  discuss the asymptotic behaviour of sequences of Hurwitz stable polynomials.




This talk is part of the Isaac Newton Institute Seminar Series series.

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