Geodesic
Some new criteria for uniform approximability of functions by rational fractions
Sbornik. Mathematics, Tome 186 (1995) no. 9, pp. 1325-1340 
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/
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     title = {Some new criteria for uniform approximability of functions by rational fractions},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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