Geodesic
Uniform Approximation of Functions by Polynomial Solutions to Second-Order Elliptic Equations on Compact Sets in $\mathbb{R}^2$
Matematičeskie zametki, Tome 74 (2003) no. 1, pp. 41-51 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we study necessary and sufficient conditions for functions to be approximated uniformly on plane compact sets by polynomial solutions to second-order homogeneous elliptic equations with constant coefficients. Sufficient conditions for approximability are of reductive character, i.e., the possibility of approximating on some (simpler) parts of the compact set implies approximability on the entire compact set. 
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     title = {Uniform {Approximation} of {Functions} by {Polynomial} {Solutions} to {Second-Order} {Elliptic} {Equations} on {Compact} {Sets} in $\mathbb{R}^2$},
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A. B. Zaitsev. Uniform Approximation of Functions by Polynomial Solutions to Second-Order Elliptic Equations on Compact Sets in $\mathbb{R}^2$. Matematičeskie zametki, Tome 74 (2003) no. 1, pp. 41-51. http://geodesic.mathdoc.fr/item/MZM_2003_74_1_a4/

[1] Zaitsev A. B., “O ravnomernoi priblizhaemosti funktsii polinomami spetsialnykh klassov na kompaktakh v $\mathbb{R}^2$”, Matem. zametki, 71:1 (2002), 75–87 | MR | Zbl

[2] Paramonov P. V., Fedorovskii K. Yu., “O ravnomernoi i $C^1$-priblizhaemosti funktsii na kompaktakh v $\mathbb{R}^2$ resheniyami ellipticheskikh uravnenii vtorogo poryadka”, Matem. sb., 190:2 (1999), 123–144 | MR | Zbl

[3] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. Funktsionalnyi analiz, Mir, M., 1977 | MR

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

[5] Bishop E., “Granichnye mery analiticheskikh differentsialov”, Nekotorye voprosy teorii priblizhenii, IL, M., 1963, 87–100

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

[7] Fedorovskii K. Yu., “O ravnomernykh priblizheniyakh funktsii $n$-analiticheskimi polinomami na spryamlyaemykh konturakh v $\mathbb C$”, Matem. zametki, 59:4 (1996), 604–610 | MR | Zbl

[8] Carmona J. J., Fedorovski K. Yu., Paramonov P. V., On Uniform Approximation by Polyanalytic Polynomials and the Dirichlet Problem for Bianalytic Functions, Preprint No 415, Centre de Recerca Matematica, Barcelona, Spain, 1999 | MR

[9] Paramonov P. V., Verdera J., “Approximation by solutions of elliptic equations on closed subsets of euclidean space”, Math. Scand., 74:2 (1994), 249–259 | MR | Zbl

[10] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR | Zbl