Geodesic
Uniform Approximation of Functions Continuous on a Compact Subset of $\mathbb C$ and Analytic in Its Interior by Functions Bianalytic in Its Neighborhoods
Matematičeskie zametki, Tome 69 (2001) no. 2, pp. 245-261 
M. Ya. Mazalov. Uniform Approximation of Functions Continuous on a Compact Subset of $\mathbb C$ and Analytic in Its Interior by Functions Bianalytic in Its Neighborhoods. Matematičeskie zametki, Tome 69 (2001) no. 2, pp. 245-261. http://geodesic.mathdoc.fr/item/MZM_2001_69_2_a8/
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     title = {Uniform {Approximation} of {Functions} {Continuous} on a {Compact} {Subset} of $\mathbb C$ and {Analytic} in {Its} {Interior} by {Functions} {Bianalytic} in {Its} {Neighborhoods}},
     journal = {Matemati\v{c}eskie zametki},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that an arbitrary function continuous on a compact set $X\subset\mathbb C$ and holomorphic in the interior of $X$ can be approximated by functions bianalytic in neighborhoods of $X$ with arbitrary accuracy.

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

[2] Balk M. B., “Polianaliticheskie funktsii i ikh obobscheniya”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 85, VINITI, M., 1991, 187–246 | MR

[3] Verdera J., “On the uniform approximation problem for the square of the Cauchy–Riemann operator”, Pacific J. Math., 159 (1993), 379–396 | MR | Zbl

[4] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR | Zbl

[5] Harvey R., Polking J., “Removable singularities of solutions of linear partial differential equations”, Acta Math., 125 (1970), 39–56 | DOI | MR | Zbl

[6] David G., “Opérateurs intégraux singuliers sur certaines corbes du plan complexe”, Ann. sci. E. N. S., 17:1 (1984), 157–189 | MR | Zbl

[7] Nguyen Xuan Uy, “An extremal problem on singular integrals”, Amer. J. Math., 102:2 (1980), 279–290 | DOI | MR | Zbl

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

[9] Paramonov P. V., “Nekotorye novye kriterii ravnomernoi priblizhaemosti funktsii ratsionalnymi drobyami”, Matem. sb., 186:9 (1995), 97–112 | MR | Zbl