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

Epithelium

過去分詞

,Abel’s Equations,In this chapter we study the structure of the set of curves . associated with real polynomials of degree . by means of the Chebyshev correspondence.

graphy

Computations in Moduli Spaces,First 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.

Mundane

1439-7382 .Contains many pictures which visualize involved theory.Desc.The problems of conditional optimization of the uniform (or C-) norm for polynomials and rational functions arise in various branches of science and technology. Their numerical solution is notoriously difficult in case of high degree funct

整頓

勉勵

Least Deviation Problems,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.

老巫婆

Subjugate

Cell Decomposition of the Moduli Space,e as functions of a point . in the moduli space. In this chapter we develop a combinatorial geometric approach to the investigation of the period map. To curves . in the moduli space we shall assign in a one-to-one fashion trees . of a special form with edges labelled by positive numbers.

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The Problem of the Optimal Stability Polynomial,. Our analysis of the optimization Problem B in Chap. 1 enables us to figure out the characteristic features of the solution. We know that the optimal stability polynomial has many alternance points, so its extremality parameter . is not large.

冷漠