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Extremal Properties of Polynomials

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A Panorama of Hungarian Mathematics in the Twentieth Century I

Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 14))

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Abstract

This article focuses on those problems about extremal properties of polynomials that were considered by the Hungarian mathematicians Lipót Fejér, Mihály Fekete, Marcel Riesz, Alfréd Rényi, György Pólya, Gábor Szegő, Pál Erdős, Pál Turán, Géza Freud, Gábor Somorjai, and their associates, who lived and died mostly in the twentieth century. It reflects my personal taste and is far from complete even within the subdomains we focus on most, namely inequalities for polynomials with constraints, Müntz polynomials, and the geometry of polynomials. There are separate chapters of this book devoted to orthogonal polynomials, interpolation, and function series, so here we touch these issues only marginally.

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  1. Department of Mathematics, Texas A&M University, College Station, Texas, 77843, USA

    Tamás Erdélyi

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  1. Tamás Erdélyi
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  1. Department of Mathematics, University of Maryland, College Park, MD, 20742-4015, USA

    János Horváth

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Erdélyi, T. (2006). Extremal Properties of Polynomials. In: Horváth, J. (eds) A Panorama of Hungarian Mathematics in the Twentieth Century I. Bolyai Society Mathematical Studies, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30721-1_5

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