G.V. Milovanovi'c, D.S. Mitrinovi'c and Th. M. Rassias, Topics in polynomials: extremal problems, inequalities, zeros, World Scientific, Singapore, 1994. Home/Search Document Not in Database Summary Related Articles Check |
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Chebyshev-Laurent Polynomials and Weighted Approximation - de Andrade, al. (1998) (Correct)
....proved a Jackson type theorem for approximation by Sn polynomials. An important question in Approximation Theory is to establish inverse type theorems. Basic tools for proving such theorems for approximation by algebraic polynomials are the inequalities of Markov [11] and Bernstein [1] see also [12, 14]) It is known that Markov s and Bernstein s inequalities are sharp in the sence that there exist extremal polynomials for which equalities are attained. In fact, in both cases the extremal polynomial is the Chebyshev one. Chebyshev polynomials are solutions of some other interesting extremal ....
....[10] proved also that the Chebyshev polynomial Tn is the longest one among all algebraic polynomials whose modulus is bounded by one in [ Gamma1; 1] thus verifying a long standing conjecture of Erdos. For these and many other interesting extremal problems for algebraic polynomials we refer to [12] and [14] ....
G.V.Milovanovi'c, D.S. Mitrinovi'c and Th.R. Rassias, Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific, Singapore, 1994.
Chebyshev Polynomials With Integer Coefficients - Pritsker (Correct)
.... interval [a; b] ae R by kfk [a;b] max x2[a;b] jf(x)j: It is very well known that the Chebyshev polynomial T n (x) 2 1 Gamman cos(n arccos x) is a monic polynomial of degree n, which minimizes the uniform norm on [ Gamma1; 1] in the class of all monic polynomials from P n (C) see [2] [12] and 1991 AMS Subject Classification. Primary 30C10, 11C08; Secondary 31A05, 31A15. Key words and phrases. Chebyshev polynomials; Integer Chebyshev constant; Integer transfinite diameter; Multiple factors; Asymptotics; Potentials; Weighted polynomials. y Research supported in part by the ....
.... n ; n 2 N; 1.1) and the Chebyshev constant for [a; b] is given by cheb( a; b] lim n 1 kt n k 1=n [a;b] b Gamma a 4 : 1.2) Chebyshev polynomials and Chebyshev constant represent very classical topics in analysis. These ideas have applications in many areas of mathematics, see [2] [12] and [15] We remark that the Chebyshev constant of a compact set in C is equal to its transfinite diameter and to its logarithmic capacity (cf. 18, pp. 71 75] for the general definitions and a discussion) A corresponding minimization problem in the class of polynomials with integer coefficients ....
G. V. Milovanovi'c, D. S. Mitrinovi'c and Th. M. Rassias, Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific, Singapore, 1994.
Higher Order Turán Inequalities - Dimitrov (Correct)
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G.V. Milovanovi'c, D.S. Mitrinovi'c and Th. M. Rassias, Topics in polynomials: extremal problems, inequalities, zeros, World Scientific, Singapore, 1994.
Optimal Oscillation Points For Polynomials Of.. - Lawrence Harris.. (Correct)
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G. V. Milovanovi'c, D. S. Mitrinovi'c, Th. M. Rassias, Topics In Polynomials: Extremal Problems, Inequalities, Zeros,World Scientific, Singapore, 1994.
Coefficients of Polynomials of Restricted Growth on the Real Line - Harris (Correct)
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G. V. Milovanovi'c, D. S. Mitrinovi'c, Th. M. Rassias, Topics In Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific, Singapore 1994.
Optimal Oscillation Points For Polynomials Of Restricted Growth.. - Harris (Correct)
No context found.
G. V. Milovanovi'c, D. S. Mitrinovi'c, Th. M. Rassias, Topics In Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific, Singapore, 1994.
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