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Comptes Rendus Mathématique
Volume 353, n° 1
pages 5-9 (janvier 2015)
Doi : 10.1016/j.crma.2014.10.011
Received : 10 Mars 2014 ;  accepted : 16 October 2014
On Bernstein and Erdős–Lax's inequalities for quaternionic polynomials
Sur les inégalités de Bernstein et de Erdős–Lax pour les polynômes quaternioniques

Sorin G. Gal a , Irene Sabadini b
a University of Oradea, Department of Mathematics and Computer Science, Str. Universitatii Nr. 1, 410087 Oradea, Romania 
b Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy 


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.

The full text of this article is available in PDF format.

Dans cet article, l'inégalité de Bernstein, bien connue pour les polynômes de  , 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.

The full text of this article is available in PDF format.

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