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Asymptotic zero distribution for a class of extremal polynomials

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URI: https://hdl.handle.net/10016/33955
ISSN: 1664-3607
DOI: https://doi.org/10.1142/S166436071950019X
UXXI: AR/0000026478
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Asymptotic_BMS_2020.pdf (258.26 KB)
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2021-04
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World Scientific Publishing Company
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Abstract
We consider extremal polynomials with respect to a Sobolev-type p-norm, with 1and measures supported on compact subsets of the real line. For a wide class of such extremal polynomials with respect to mutually singular measures (i.e. supported on disjoint subsets of the real line), it is proved that their critical points are simple and contained in the interior of the convex hull of the support of the measures involved and the asymptotic critical point distribution is studied. We also find the nth root asymptotic behavior of the corresponding sequence of Sobolev extremal polynomials and their derivatives.
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Extremal polynomials, Sobolev orthogonality, Location of zeros, Asymptotic behavior
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Díaz González, A., López Lagomasino, G. & Pijeira Cabrera, H. (2020). Asymptotic zero distribution for a class of extremal polynomials. Bulletin of Mathematical Sciences, 11(01), 1950019.
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