Geodesic
Polynomials with a Prescribed Zero and the Bernstein's Inequality
Canadian journal of mathematics, Tome 45 (1993) no. 3, pp. 627-637

Voir la notice de l'article provenant de la source Cambridge University Press

Let be the class of all polynomials/? of degree at most n such that In view of the example zn it follows from Bernstein's inequality for polynomials that at each point z0 of the unitcirle. It was shown by A. Giroux and Q. I. Rahman [2] that if denotes the subclass of polynomials in which vanish at 1, then where c 1 and c 2 are constants not depending on n. Here we find the exact value of which has some special significance and also at certain other points of the unit circle.
DOI : 10.4153/CJM-1993-034-3
Mots-clés : 30C10, 26D05, 41A17, polynomials, Bernstein's inequality, Chebyshev polynomials 
Olivier, P. F.; Watt, A. O. Polynomials with a Prescribed Zero and the Bernstein's Inequality. Canadian journal of mathematics, Tome 45 (1993) no. 3, pp. 627-637. doi: 10.4153/CJM-1993-034-3
@article{10_4153_CJM_1993_034_3,
     author = {Olivier, P. F. and Watt, A. O.},
     title = {Polynomials with a {Prescribed} {Zero} and the {Bernstein's} {Inequality}},
     journal = {Canadian journal of mathematics},
     pages = {627--637},
     year = {1993},
     volume = {45},
     number = {3},
     doi = {10.4153/CJM-1993-034-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-034-3/}
}
TY  - JOUR
AU  - Olivier, P. F.
AU  - Watt, A. O.
TI  - Polynomials with a Prescribed Zero and the Bernstein's Inequality
JO  - Canadian journal of mathematics
PY  - 1993
SP  - 627
EP  - 637
VL  - 45
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-034-3/
DO  - 10.4153/CJM-1993-034-3
ID  - 10_4153_CJM_1993_034_3
ER  - 
%0 Journal Article
%A Olivier, P. F.
%A Watt, A. O.
%T Polynomials with a Prescribed Zero and the Bernstein's Inequality
%J Canadian journal of mathematics
%D 1993
%P 627-637
%V 45
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1993-034-3/
%R 10.4153/CJM-1993-034-3
%F 10_4153_CJM_1993_034_3

[1] 1. Frappier, C., Rahman, Q. I. and St. Ruscheweyh, On polynomials with a prescribed zero, Constr. Approx. 2(1986), 171–177. Google Scholar

[2] 2. Giroux, A. and Rahman, Q. I., Inequalities for polynomials with a pre scribed zero, Trans. Amer. Math. Soc. 193(1974), 67–98. Google Scholar

Cité par Sources :