Geodesic
On Polynomials of Best Approximation
Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 631-636.

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

In the space of continuous functions defined on the ball from $\mathbb R^n$, $n\ge2$, we study the set of algebraic polynomials of least deviation from zero. Its width and dimension are estimated.
Keywords: algebraic polynomial of least deviation from zero, Chebyshev polynomial, trigonometric polynomial, Bézout theorem
Mots-clés : orthogonal transformation. 
@article{MZM_2007_82_4_a17,
     author = {V. A. Yudin},
     title = {On {Polynomials} of {Best} {Approximation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {631--636},
     publisher = {mathdoc},
     volume = {82},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a17/}
}
TY  - JOUR
AU  - V. A. Yudin
TI  - On Polynomials of Best Approximation
JO  - Matematičeskie zametki
PY  - 2007
SP  - 631
EP  - 636
VL  - 82
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a17/
LA  - ru
ID  - MZM_2007_82_4_a17
ER  - 
%0 Journal Article
%A V. A. Yudin
%T On Polynomials of Best Approximation
%J Matematičeskie zametki
%D 2007
%P 631-636
%V 82
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a17/
%G ru
%F MZM_2007_82_4_a17
V. A. Yudin. On Polynomials of Best Approximation. Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 631-636. http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a17/

[1] P. L. Chebyshev, Polnoe sobranie sochinenii, Izd-vo AN SSSR, M.–L., 1948 | MR | Zbl

[2] W. B. Gearhart, “Some Chebyshev approximations by polynomials in two variables”, J. Approx. Theory, 8:3 (1973), 195–209 | DOI | MR | Zbl

[3] V. A. Yudin, “Naimenee uklonyayuschiesya ot nulya mnogochleny”, Matem. zametki, 78:2 (2005), 308–313 | MR | Zbl

[4] R. Uoker, Algebraicheskie krivye, IL, M., 1952 | MR | Zbl

[5] N. N. Andreev, V. A. Yudin, “Naimenee uklonyayuschiesya ot nulya mnogochleny i kubaturnye formuly chebyshevskogo tipa”, Funktsionalnye prostranstva, garmonicheskii analiz, differentsialnye uravneniya, Tr. MIAN, 232, Nauka, M., 2001, 45–57 | MR | Zbl

[6] N. N. Andreev, V. A. Yudin, “Best approximation of polynomials on the sphere and on the ball”, Recent Progress in Multivariate Approximation, Proceedings of the 4th International Conference, Witten–Bommerholz, Germany, September 24–29, 2000, Internat. Ser. Numer. Math., 137, Birkhäuser, Basel, 2001, 23–30 | MR | Zbl

[7] Yuan Xu, “On polynomials of least deviation from zero in several variables”, Experiment. Math., 13:1 (2004), 103–112 | MR | Zbl

[8] I. Mairhuber, “On Haar's theorem concerning Chebysheff approximation problems having unique solutions”, Proc. Amer. Math. Soc., 7 (1956), 609–615 | DOI | MR | Zbl