no. 21-22
Numerical analysis
Approximation by Müntz spaces on positive intervals
[Approximation par espaces de Müntz sur un intervalle positif]

Présenté par : Philippe G. Ciarlet

Ait-Haddou, Rachid1 ; Mazure, Marie-Laurence2
1 Geometric Modeling and Scientific Visualization Center, King Abdullah University of Science and Technology, Saudi Arabia
2 Laboratoire Jean-Kuntzmann, Université Joseph-Fourier, BP 53, 38041 Grenoble cedex 9, France
Comptes Rendus. Mathématique, Tome 351 (2013) no. 21-22, pp. 849-852.

En 1912, les opérateurs dits de Bernstein permirent à S.N. Bernstein de donner une preuve constructive du théorème de Weierstrass. Nous étendons ce résultat aux espaces de Müntz sur des intervalles positifs.

The so-called Bernstein operators were introduced by S.N. Bernstein in 1912 to give a constructive proof of Weierstrassʼ theorem. We show how to extend his result to Müntz spaces on positive intervals.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.10.018
Ait-Haddou, Rachid 1 ; Mazure, Marie-Laurence 2

1 Geometric Modeling and Scientific Visualization Center, King Abdullah University of Science and Technology, Saudi Arabia
2 Laboratoire Jean-Kuntzmann, Université Joseph-Fourier, BP 53, 38041 Grenoble cedex 9, France 
@article{CRMATH_2013__351_21-22_849_0,
     author = {Ait-Haddou, Rachid and Mazure, Marie-Laurence},
     title = {Approximation by {M\"untz} spaces on positive intervals},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {849--852},
     publisher = {Elsevier},
     volume = {351},
     number = {21-22},
     year = {2013},
     doi = {10.1016/j.crma.2013.10.018},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2013.10.018/}
}
TY  - JOUR
AU  - Ait-Haddou, Rachid
AU  - Mazure, Marie-Laurence
TI  - Approximation by Müntz spaces on positive intervals
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 849
EP  - 852
VL  - 351
IS  - 21-22
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2013.10.018/
DO  - 10.1016/j.crma.2013.10.018
LA  - en
ID  - CRMATH_2013__351_21-22_849_0
ER  - 
%0 Journal Article
%A Ait-Haddou, Rachid
%A Mazure, Marie-Laurence
%T Approximation by Müntz spaces on positive intervals
%J Comptes Rendus. Mathématique
%D 2013
%P 849-852
%V 351
%N 21-22
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2013.10.018/
%R 10.1016/j.crma.2013.10.018
%G en
%F CRMATH_2013__351_21-22_849_0
Ait-Haddou, Rachid; Mazure, Marie-Laurence. Approximation by Müntz spaces on positive intervals. Comptes Rendus. Mathématique, Tome 351 (2013) no. 21-22, pp. 849-852. doi : 10.1016/j.crma.2013.10.018. http://www.numdam.org/articles/10.1016/j.crma.2013.10.018/

[1] Ait-Haddou, R. Dimension elevation in Müntz spaces: a new emergence of the Müntz condition (in press) | arXiv

[2] Ait-Haddou, R.; Sakane, Y.; Nomura, T. A Müntz type theorem for a family of corner cutting schemes, Comput. Aided Geom. Design, Volume 30 (2013), pp. 240-253

[3] Aldaz, J.M.; Kounchev, O.; Render, H. Bernstein operators for exponential polynomials, Constr. Approx., Volume 20 (2009), pp. 345-367

[4] Almira, J.M. Müntz type theorems I, Surv. Approx. Theory, Volume 3 (2007), pp. 152-194

[5] Bernstein, S.N. Démonstration du théorème de Weierstrass fondée sur le calcul des probabilités, Commun. Soc. Math. Kharkov, Volume 13 (1912), pp. 1-2

[6] Borwein, P.; Erdélyi, T. Polynomials and Polynomial Inequalities, Graduate Texts in Mathematics, vol. 161, Springer-Verlag, New York, 1995

[7] Korovkin, P.P. Linear Operators and Approximation Theory, Hindustan Publ. Corp., 1960

[8] Mazure, M.-L. Bernstein-type operators in Chebyshev spaces, Numer. Algorithms, Volume 52 (2009), pp. 93-128

[9] Mazure, M.-L. Finding all systems of weight functions associated with a given Extended Chebyshev space, J. Approx. Theory, Volume 163 (2011), pp. 363-376

Cité par Sources :