Titlebook: Extremal Polynomials and Riemann Surfaces; Andrei Bogatyrev Book 2012 Springer-Verlag Berlin Heidelberg 2012 Pell-Abel equation.Riemann su

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https://doi.org/10.1007/978-3-642-25634-9Pell-Abel equation; Riemann surface; Schottky model; extremal polynomials; least deviation problems

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Andrei BogatyrevIncludes numerous problems and exercises which provide a deep insight in the subject and allow to conduct independent research in this topic.Contains many pictures which visualize involved theory.Desc

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Springer Monographs in Mathematicshttp://image.papertrans.cn/f/image/320014.jpg

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,Haltestelle Ω: aktueller Einblick,t we investigate least deviation problems using methods of convex analysis. We deduce a generalized alternation principle which completely characterizes solutions of such problems. In giving the definition of an extremal polynomial in the introduction we were motivated by this principle.

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https://doi.org/10.1007/978-981-10-2486-3In this chapter we study the structure of the set of curves . associated with real polynomials of degree . by means of the Chebyshev correspondence.

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Xiaoxia Sun,Yu Jin,Xiaoxin HuangFirst of all, for an effective calculation of extremal polynomials we require the solution of Abel’s (6.1) defined on the universal cover of the moduli space. These equations have been thoroughly investigated in Chap. 5; here we present only the details required for computations.