Comptes Rendus
no. 1
Complex analysis
On Bernstein and Erdős–Lax's inequalities for quaternionic polynomials
[Sur les inégalités de Bernstein et de Erdős–Lax pour les polynômes quaternioniques]

Présenté par : Jean-Pierre Demailly

Sorin G. Gal1 ; Irene Sabadini2
1 University of Oradea, Department of Mathematics and Computer Science, Str. Universitatii Nr. 1, 410087 Oradea, Romania
2 Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy
Comptes Rendus. Mathématique, Volume 353 (2015) no. 1, pp. 5-9.

Dans cet article, l'inégalité de Bernstein, bien connue pour les polynômes de C, est prouvée pour les polynômes quaternioniques. Nous démontrons que l'inégalité de Erdős–Lax n'est pas valide, en général, mais qu'elle est valide pour un ensemble particulier de polynômes.

In this paper the well-known Bernstein's inequality for complex polynomials is extended to the quaternionic setting. We also show that the Erdős–Lax's inequality does not hold in general, but it works for a particular class of polynomials.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.10.011
Sorin G. Gal 1 ; Irene Sabadini 2

1 University of Oradea, Department of Mathematics and Computer Science, Str. Universitatii Nr. 1, 410087 Oradea, Romania
2 Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy 
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Sorin G. Gal; Irene Sabadini. On Bernstein and Erdős–Lax's inequalities for quaternionic polynomials. Comptes Rendus. Mathématique, Volume 353 (2015) no. 1, pp. 5-9. doi : 10.1016/j.crma.2014.10.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.10.011/

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[9] M. Riesz Eine trigonometrische interpolationsformel und einige ungleichungen für polynome, Jahresber. Dtsch. Math.-Ver., Volume 23 (1914), pp. 354-368

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