Geodesic
Some new criteria for uniform approximability of functions by rational fractions
Sbornik. Mathematics, Tome 186 (1995) no. 9, pp. 1325-1340 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper Vitushkin's localization scheme for uniform rational approximation of functions is further improved. Using this result new criteria for the approximability of functions by rational fractions in the uniform and Holder metrics on compact subsets of $\mathbb C$ are obtained. 
@article{SM_1995_186_9_a5,
     author = {P. V. Paramonov},
     title = {Some new criteria for uniform approximability of functions by rational fractions},
     journal = {Sbornik. Mathematics},
     pages = {1325--1340},
     year = {1995},
     volume = {186},
     number = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_9_a5/}
}
TY  - JOUR
AU  - P. V. Paramonov
TI  - Some new criteria for uniform approximability of functions by rational fractions
JO  - Sbornik. Mathematics
PY  - 1995
SP  - 1325
EP  - 1340
VL  - 186
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/SM_1995_186_9_a5/
LA  - en
ID  - SM_1995_186_9_a5
ER  - 
%0 Journal Article
%A P. V. Paramonov
%T Some new criteria for uniform approximability of functions by rational fractions
%J Sbornik. Mathematics
%D 1995
%P 1325-1340
%V 186
%N 9
%U http://geodesic.mathdoc.fr/item/SM_1995_186_9_a5/
%G en
%F SM_1995_186_9_a5
P. V. Paramonov. Some new criteria for uniform approximability of functions by rational fractions. Sbornik. Mathematics, Tome 186 (1995) no. 9, pp. 1325-1340. http://geodesic.mathdoc.fr/item/SM_1995_186_9_a5/

[1] Vitushkin A. G., “Analiticheskaya emkost mnozhestv v zadachakh teorii priblizhenii”, UMN, 22:6 (1967), 141–199 | MR

[2] Gamelin T., Ravnomernye algebry, Mir, M., 1973 | Zbl

[3] Paramonov P. V., “O garmonicheskikh approksimatsiyakh v $C^1$-norme”, Matem. sb., 181:10 (1990), 1341–1365 | MR

[4] O'Farrell A. G., “Estimates for capacities and approximation in Lipschitz norms”, J. Reine Angew. Math., 311/312 (1979), 101–115 | MR | Zbl

[5] O'Farrell A. G., “Rational approximation and weak analyticity, II”, Math. Ann., 281 (1988), 169–176 | DOI | MR | Zbl

[6] O'Farrell A. G., “Rational approximation in Lipschitz norms, II”, Proc. Royal. Irish. Acad., 79A:11 (1979), 103–114 | MR

[7] Verdera J., “On $C^m$-rational approximation”, Proc. Amer. Math. Soc., 97:4 (1986), 621–625 | DOI | MR | Zbl

[8] Verdera J., Removability, capacity and approximation, Preprint No 1, Universitat Autonoma de Barcelona, 1994 | MR | Zbl

[9] Melnikov M. S., “Otsenka integrala Koshi po analiticheskoi krivoi”, Matem. sb., 71:4 (1966), 503–513 | MR

[10] Verdera J., “$C^m$-approximation by solutions of elliptic equations, and Calderon–Zygmund operators”, Duke Math., 55 (1987), 157–187 | DOI | MR | Zbl