Comptes Rendus
Complex analysis
On a family of extremal polynomials
Comptes Rendus. Mathématique, Volume 357 (2019) no. 7, pp. 591-596.

For a pair of conjugate trigonometrical polynomials C(t)=j=1Najcosjt, S(t)=j=1Najsinjt with real coefficients and normalization a1=1 the following extremal value is found:

An application of this result in geometric complex analysis is shown. Several conjectures for a number of extremal problems on classes of polynomials are suggested.

Pour une paire de polynômes trigonométriques C(t)=j=1Najcosjt, S(t)=j=1Najsinjt à coefficients réels avec la normalisation a1=1, on trouve la valeur extrémale

Une application en analyse géométrique complexe est montrée. On formule quelques conjectures pour les problèmes extrémaux sur les classes de polynômes.

Published online:
DOI: 10.1016/j.crma.2019.06.010

Dmitriy Dmitrishin 1; Andrey Smorodin 1; Alex Stokolos 2

1 Odessa National Polytechnic University, 1 Shevchenko Ave., Odessa 65044, Ukraine
2 Georgia Southern University, Statesboro, GA 30460, USA
     author = {Dmitriy Dmitrishin and Andrey Smorodin and Alex Stokolos},
     title = {On a family of extremal polynomials},
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Dmitriy Dmitrishin; Andrey Smorodin; Alex Stokolos. On a family of extremal polynomials. Comptes Rendus. Mathématique, Volume 357 (2019) no. 7, pp. 591-596. doi : 10.1016/j.crma.2019.06.010.

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