Geodesic
On Polynomials with Curved Majorants
Canadian journal of mathematics, Tome 34 (1982) no. 4, pp. 961-968

Voir la notice de l'article provenant de la source Cambridge University Press

A well-known result of Chebyshev is that if pn ∊ Pn , (Pn is the set of polynomials of degree at most n) and (1) then an(pn), the leading coefficient of pn , satisfies (2) with equality holding only for pn = ±Tn , where Tn is the Chebyshev polynomial of degree n. (See [6, p. 57].) This is an example of an extremal problem in which the norm of a given linear operator on Pn is sought. Another example is A. A. Markov's result that (1) implies that (3) There are also results for the linear functionals pn(k) (x 0), x 0 real, k = 1, ... n – 1 ([8]).Suppose φ(x) ≧ 0 on [–1, 1] and (1) is generalized to as suggested by Rahman [4] (polynomials with curved majorants), what can then be said about the analogue of (3) or similar extremal problems? 
Newman, D. J.; Rivlin, T. J. On Polynomials with Curved Majorants. Canadian journal of mathematics, Tome 34 (1982) no. 4, pp. 961-968. doi: 10.4153/CJM-1982-069-9
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