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@article{IM2_2004_68_3_a2, author = {A. Boivin and P. M. Gauthier and P. V. Paramonov}, title = {On uniform approximation by $n$-analytic functions on closed sets in~$\mathbb C$}, journal = {Izvestiya. Mathematics }, pages = {447--459}, publisher = {mathdoc}, volume = {68}, number = {3}, year = {2004}, language = {en}, url = {http://geodesic.mathdoc.fr/item/IM2_2004_68_3_a2/} }
TY - JOUR AU - A. Boivin AU - P. M. Gauthier AU - P. V. Paramonov TI - On uniform approximation by $n$-analytic functions on closed sets in~$\mathbb C$ JO - Izvestiya. Mathematics PY - 2004 SP - 447 EP - 459 VL - 68 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IM2_2004_68_3_a2/ LA - en ID - IM2_2004_68_3_a2 ER -
A. Boivin; P. M. Gauthier; P. V. Paramonov. On uniform approximation by $n$-analytic functions on closed sets in~$\mathbb C$. Izvestiya. Mathematics , Tome 68 (2004) no. 3, pp. 447-459. http://geodesic.mathdoc.fr/item/IM2_2004_68_3_a2/
[1] Karmona Kh. Kh., Paramonov P. V., Fedorovskii K. Yu., “O ravnomernoi approksimatsii polianaliticheskimi mnogochlenami i zadache Dirikhle dlya bianaliticheskikh funktsii”, Matem. sb., 193:10 (2002), 75–98 | MR
[2] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, M.–L., 1950
[3] Kusis P., Vvedenie v teoriyu prostranstv $H_p$, Mir, M., 1984 | MR
[4] Gauthier P. M., Hengartner W., “Local harmonic majorants of functions subharmonic in the unit disc”, J. Anal. Math., 26 (1973), 405–412 | DOI | MR | Zbl
[5] Shapiro H. S., The Schwarz Function and its Generalization to Higher Dimensions, Univ. of Arkansas, Wiley – N.Y., 1992 | MR
[6] Arakelyan N. U., “Ravnomernaya approksimatsiya na zamknutykh mnozhestvakh tselymi funktsiyami”, Izv. AN SSSR. Ser. matem., 28:5 (1964), 1187–1206 | MR | Zbl
[7] Nersesyan A. A., “Ravnomernaya i kasatelnaya approksimatsiya meromorfnymi funktsiyami”, Izv. AN ArmSSR. Ser. matem., 7 (1972), 405–412 | MR
[8] Gaier D., Lektsii po teorii approksimatsii v kompleksnoi oblasti, Mir, M., 1986 | MR | Zbl
[9] Gardiner S. J., Harmonic Approximation, LMS. Lecture Notes Series, 221, Cambridge Univ. Press, Cambridge, 1995 | MR
[10] Gamelin T. V., Ravnomernye algebry, Mir, M., 1973 | Zbl
[11] Vitushkin A. G., “Analiticheskaya emkost mnozhestv v zadachakh teorii priblizhenii”, UMN, 22:6 (1967), 141–199 | MR
[12] Paramonov P. V., Verdera J., “Approximation by solutions of elliptic equations on closed subsets of euclidean space”, Math. Scand., 74 (1994), 249–259 | MR | Zbl
[13] Carmona J. J., “Mergelyan approximation theorem for rational modules”, J. Approx. Theory, 44 (1985), 113–126 | DOI | MR | Zbl
[14] Bishop E., “Granichnye mery analiticheskikh differentsialov”, Nekotorye voprosy teorii priblizhenii, IL, M., 1963, 87–100
[15] Boivin A., Gauthier P. M., Paramonov P. V., “Approximation on closed sets by analytic or meromorphic solutions of elliptic equations and applications”, Canad. J. Math., 54:5 (2002), 945–969 | MR | Zbl