Geodesic
Short note on Bernstein's Inequality
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 476-479.

Voir la notice de l'article provenant de la source Math-Net.Ru

The famous Bernstein’s inequality estimates the absolute value of a polynomial's derivative on the unit circle via the maximum absolute value of that polynomial over the circle. In this paper, we prove an explicit formula for increment of a polynomial along a ray, which allows to replace the maximum of absolute value over the unit circle by the maximum through the vertices of an inscribed regular polygon. As a consequence, a new proof of a discrete variant of Bernstein’s polynomial inequality is given.
Keywords: Polynomials, Bernstein's inequality, Growth. 
@article{SEMR_2010_7_a32,
     author = {S. A. Baba and A. L. Wani},
     title = {Short note on {Bernstein's} {Inequality}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {476--479},
     publisher = {mathdoc},
     volume = {7},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2010_7_a32/}
}
TY  - JOUR
AU  - S. A. Baba
AU  - A. L. Wani
TI  - Short note on Bernstein's Inequality
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2010
SP  - 476
EP  - 479
VL  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2010_7_a32/
LA  - en
ID  - SEMR_2010_7_a32
ER  - 
%0 Journal Article
%A S. A. Baba
%A A. L. Wani
%T Short note on Bernstein's Inequality
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2010
%P 476-479
%V 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2010_7_a32/
%G en
%F SEMR_2010_7_a32
S. A. Baba; A. L. Wani. Short note on Bernstein's Inequality. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 476-479. http://geodesic.mathdoc.fr/item/SEMR_2010_7_a32/

[1] W. Rogosinski and G. Szego, “Über die Abschnitte von Potenzreihen die in einen Kreise beschränkt bleiben”, Math. Z., 28 (1928), 73–94 | DOI | MR | Zbl

[2] A. C. Schaeffer, “Inequalities of A. Markoff and S. Bernstein for polynomials and related functions”, Bull. Amer. Math. Soc., 47 (1941), 565–579 | DOI | MR

[3] C. Frappier, Q. I. Rahmau, St. Ruscheweyh, “New inequalities for polynomials”, Trans. Amer. Math. Society, 288 (1985), 69–99 | DOI | MR | Zbl

[4] D. Dryanov, R. Fournier, “On discrete vatriant of Bernstein inequality”, J. Aprox. Theory, 136 (2005), 84–90 | DOI | MR | Zbl