Geodesic
Uniform approximation by solutions of elliptic systems
Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 351-377 Cet article a éte moissonné depuis la source Math-Net.Ru

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An analogue of the theorem of Vitushkin (RZh. Mat., 1968, 6Б202) is proved for the problem of uniform approximation by solutions of homogeneous elliptic systems of differential equations with constant coefficients. Bibliography: 20 titles. 
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N. N. Tarkhanov. Uniform approximation by solutions of elliptic systems. Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 351-377. http://geodesic.mathdoc.fr/item/SM_1988_61_2_a5/

[1] Mergelyan S. N., “Ravnomernye priblizheniya funktsii kompleksnogo peremennogo”, UMN, 7:2 (1952), 31–122 | MR | Zbl

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

[3] Lax P., “A stability theory of abstract differential equations and its applications to the study of local behaviors of solutions of elliptic equations”, Commun. Pure Appl. Math., 8 (1956), 747–766 | DOI | MR

[4] Malgrange B., “Existence et approximation des solutions des equations aux derivees partielles et des equations de convolutions”, Ann. Inst. Fourier (Grenoble), 6 (1955–1956), 271–355 | MR

[5] Browder F. E., “Approximation by solutions of partial differential equation”, Amer. J. Math., 84 (1962), 134–160 | DOI | MR | Zbl

[6] Weinstock B., “Uniform approximations by solutions of elliptic equations”, Proc. Amer. Math. Soc., 41:2 (1973), 513–517 | DOI | MR | Zbl

[7] Mergelyan S. N., “O teoreme M. A. Lavrenteva”, DAN SSSR, 77:4 (1951), 565–568 | MR

[8] Grigorev Yu. M., Naumov V. V., “Approksimatsionnye teoremy dlya sistemy Moisila–Teodoresku”, Sib. matem. zhurn., 25:5 (1984), 9–19 | MR

[9] Saak E. M., “Ustoichivost zadachi o skachke dlya golomorfnogo vektora”, Ukr. matem. zhurn., 31:5 (1979), 525–531 | MR | Zbl

[10] Tarkhanov N. N., “O matritse Karlemana dlya ellipticheskikh sistem”, DAN SSSR, 284:2 (1985), 294–297 | MR | Zbl

[11] Dolzhenko E. P., “O priblizhenii na zamknutykh oblastyakh i o nul-mnozhestvakh”, DAN SSSR, 143:4 (1962), 771–774

[12] Polking J. C., “Approximation in $L_p$ by solutions of elliptic partial differential equations”, Amer. J. Math., 94:4 (1972), 1231–1244 | DOI | MR | Zbl

[13] Bagby T., “Approximation in the mean by solutions of elliptic equations”, Trans. Amer. Math. Soc., 281:2 (1984), 761–784 | DOI | MR | Zbl

[14] Burbaki N., Differentsiruemye i analiticheskie mnogoobraziya. Svodka rezultatov, Mir, M., 1975 | MR

[15] Harvey R., Polking J. C., “A Laurent expansion for solutions of elliptic equations”, Trans. Amer. Math. Soc., 180 (1973), 407–413 | DOI | MR | Zbl

[16] Grathendieck A., “Sur les espaces de solutions d'une classe generale d'equations aux derivees partielles”, J. Anal. Math., 2 (1952–1953), 243–280 | DOI | MR

[17] Harvey R., Polking J. C., “A notion of capasity which characterises removable singularities”, Trans. Amer. Math. Soc., 169 (1972), 183–195 | DOI | MR | Zbl

[18] Tarkhanov N. N., “Analog teoremy Penleve dlya ellipticheskikh sistem”, Matem. zametki., 37:4 (1985), 554–560 | MR | Zbl

[19] Harvey R., Polking J. C., “Removable singularities of solutions of linear partial differential equations”, Acta Math., 125:1–2 (1970), 39–56 | DOI | MR | Zbl

[20] Sinanyan S. O., “O svyazi mezhdu ekstremalnostyu koeffitsientov ryada Lorana i polnotoi mnozhestva analiticheskikh funktsii v prostranstve nepreryvnykh funktsii”, Matem. zametki., 15:2 (1974), 221–228 | Zbl