Geodesic
$C^m$-approximations by harmonic polynomials on compact sets in $\mathbb R^n$
Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 231-251 Cet article a éte moissonné depuis la source Math-Net.Ru

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Conditions for approximation of functions by harmonic polynomials on compact sets $X$ in $\mathbb R^n$ $(n = 2,3,\dots)$ in Whitney type norms on the spaces $C_{\mathrm{jet}}^m(X)$ $(m\geqslant 0)$ are studied in this paper. 
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P. V. Paramonov. $C^m$-approximations by harmonic polynomials on compact sets in $\mathbb R^n$. Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 231-251. http://geodesic.mathdoc.fr/item/SM_1994_78_1_a14/

[1] Walsh J. L., “The approximation of harmonic functions by harmonic polynomials and by harmonic rational functions”, Bull. Amer. Math. Soc., 35 (1929), 499–544 | DOI | MR | Zbl

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

[3] Whitney H., “Analytic extensions of differentiable functions defined in closed sets”, Trans. Amer. Math. Soc., 36 (1934), 63–89 | DOI | MR | Zbl

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

[5] Verdera J., “$C^m$-approximations by solutions of elliptic equations and Calderon-Zygmund operators”, Duke Math. J., 55:1 (1987), 157–187 | DOI | MR | Zbl

[6] O'Farrell A. G., “Rational approximations in Lipschitz norms, II”, Proc. Royal Irish Acad., 79A (1979), 104–114

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

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

[9] Keldysh M. V., “O razreshimosti i ustoichivosti zadachi Dirikhle”, UMN, 1941, no. 8, 171–231 | MR | Zbl

[10] Deny J., “Systémes totaux de functions harmoniques”, Ann. Inst. Fourier, 1 (1949), 103–113 | MR

[11] Mateu J., Orobitg J., “Lipschitz approximation by harmonic functions and some applications to spectral sinthesis”, Indiana Univ. Math. J., 39 (1990), 703–736 | DOI | MR | Zbl

[12] Johnston E. H., “The boundary modulus of continuity of harmonic functions”, Pacif. J. Math., 90:1 (1980), 87–98 | MR | Zbl

[13] Carleson L., “On the connection between Hausdorff measure and capacity”, Ark. Math., 3 (1958), 403–406 | DOI | MR | Zbl

[14] Keldysh M. V., Lavrentev M. A., “Ob ustoichivosti reshenii zadachi Dirikhle”, Izv. AN SSSR. Ser. matem., 4 (1937), 551–593

[15] Landkof N. S., Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966 | MR | Zbl

[16] Kral J., “Some extension results concerning harmonic functions”, J. London Math. Soc. (2), 28:1 (1983), 62–70 | DOI | MR | Zbl

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