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Zeros of Orthogonal Polynomials

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Orthogonal Polynomials (AIMSVSW 2018)

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Abstract

In this lecture we discuss properties of zeros of orthogonal polynomials. We review properties that have been used to derive bounds for the zeros of orthogonal polynomials. Topics to be covered include Markov’s theorem on monotonicity of zeros and its generalisations, the proof of a conjecture by Askey and its extensions, interlacing properties of zeros, Sturm’s comparison theorem and convexity of zeros.

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Authors and Affiliations

  1. Department of Decision Sciences, University of South Africa, Pretoria, South Africa

    Kerstin Jordaan

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  1. Kerstin Jordaan
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Correspondence to Kerstin Jordaan .

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Editors and Affiliations

  1. University of Yaoundé I, Yaoundé, Cameroon; African Institute for Mathematical Sciences, Limbe, Cameroon

    Mama Foupouagnigni

  2. Institute for Mathematics, University of Kassel, Kassel, Germany

    Wolfram Koepf

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Jordaan, K. (2020). Zeros of Orthogonal Polynomials. In: Foupouagnigni, M., Koepf, W. (eds) Orthogonal Polynomials. AIMSVSW 2018. Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-36744-2_17

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