Geodesic
Uniform approximation of $sgn(x)$ by rational functions with prescribed poles
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (2007) no. 1, pp. 95-108 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{JMAG_2007_3_1_a5,
     author = {F. Peherstorfer and P. Yuditskii},
     title = {Uniform approximation of $sgn(x)$ by rational functions with prescribed poles},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {95--108},
     year = {2007},
     volume = {3},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2007_3_1_a5/}
}
TY  - JOUR
AU  - F. Peherstorfer
AU  - P. Yuditskii
TI  - Uniform approximation of $sgn(x)$ by rational functions with prescribed poles
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2007
SP  - 95
EP  - 108
VL  - 3
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JMAG_2007_3_1_a5/
LA  - en
ID  - JMAG_2007_3_1_a5
ER  - 
%0 Journal Article
%A F. Peherstorfer
%A P. Yuditskii
%T Uniform approximation of $sgn(x)$ by rational functions with prescribed poles
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2007
%P 95-108
%V 3
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_2007_3_1_a5/
%G en
%F JMAG_2007_3_1_a5
F. Peherstorfer; P. Yuditskii. Uniform approximation of $sgn(x)$ by rational functions with prescribed poles. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (2007) no. 1, pp. 95-108. http://geodesic.mathdoc.fr/item/JMAG_2007_3_1_a5/

[1] N. Akhiezer, Theory of Approximation, Dover, NY, 1992 | MR

[2] N. Akhiezer, Elements of the Theory of Elliptic Functions, AMS, Providence, RI, 1990 | MR | Zbl

[3] S. Bernstein, “Sur la meilleure approximation de $\vert x\vert$ par des polynomes des degrés donnés”, Acta Math., 27 (1914), 1–57 | DOI | MR

[4] S. Bernstein, “On the Best Approximation of $\vert x\vert^p$ by Polynomials of Very High Degree”, Izv. Akad. Nauk SSSR. Ser. Mat., 2 (1938), 169–180

[5] A. Eremenko, P. Yuditskii, “Uniform Approximation of sgn$(x)$ by Polynomials and Entire Functions”, J. Anal. Math. (to appear) | MR

[6] E. I. Zolotarev, Anwendung der elliptischen Funktionen auf Probleme "uber Funktionen, die von Null am wenigsten oder am meisten abweichen, Abh. St. Petersb., XXX, 1877 | Zbl