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.
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.
Accepted:
Published online:
Sorin G. Gal 1; Irene Sabadini 2
@article{CRMATH_2015__353_1_5_0, author = {Sorin G. Gal and Irene Sabadini}, title = {On {Bernstein} and {Erd\H{o}s{\textendash}Lax's} inequalities for quaternionic polynomials}, journal = {Comptes Rendus. Math\'ematique}, pages = {5--9}, publisher = {Elsevier}, volume = {353}, number = {1}, year = {2015}, doi = {10.1016/j.crma.2014.10.011}, language = {en}, }
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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