Geodesic
Uniform Approximability of Functions by Polynomials of Special Classes on Compact Sets in $\mathbb R^2$
Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 75-87 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We derive several sufficient conditions for the uniform approximability of functions by polynomial solutions of homogeneous elliptic equations of second order with constant coefficients on Carathéodory compact sets in $\mathbb R^2$. 
@article{MZM_2002_71_1_a6,
     author = {A. B. Zaitsev},
     title = {Uniform {Approximability} of {Functions} by {Polynomials} of {Special} {Classes} on {Compact} {Sets} in $\mathbb R^2$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {75--87},
     year = {2002},
     volume = {71},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a6/}
}
TY  - JOUR
AU  - A. B. Zaitsev
TI  - Uniform Approximability of Functions by Polynomials of Special Classes on Compact Sets in $\mathbb R^2$
JO  - Matematičeskie zametki
PY  - 2002
SP  - 75
EP  - 87
VL  - 71
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a6/
LA  - ru
ID  - MZM_2002_71_1_a6
ER  - 
%0 Journal Article
%A A. B. Zaitsev
%T Uniform Approximability of Functions by Polynomials of Special Classes on Compact Sets in $\mathbb R^2$
%J Matematičeskie zametki
%D 2002
%P 75-87
%V 71
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a6/
%G ru
%F MZM_2002_71_1_a6
A. B. Zaitsev. Uniform Approximability of Functions by Polynomials of Special Classes on Compact Sets in $\mathbb R^2$. Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 75-87. http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a6/

[1] Khermander L., Analiz lineinykh differentsialnykh operatorov, Mir, M., 1986

[2] Paramonov P. V., “$C^m$-priblizheniya garmonicheskimi polinomami na kompaktnykh mnozhestvakh v $\mathbb R^n$”, Matem. sb., 184:2 (1993), 105–128 | Zbl

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

[4] O'Farrell A. G., “A generalized Walsh–Lebesgue theorem”, Proc. Roy. Soc. Edinburg. Sect. A, 73:1 (1975), 231–234 | MR | Zbl

[5] 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

[6] 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

[7] Verchota G. C, Vogel A. L., “Nonsymmetric systems on nonsmooth planar domains”, Trans. Amer. Math. Soc., 349:11 (1997), 4501–4535 | DOI | MR | Zbl

[8] Bishop E., “Struktura nekotorykh mer”, Nekotorye voprosy teorii priblizhenii, Sb., ed. A. A. Gonchar, IL, M., 1963, 74–86

[9] Bishop E., “Granichnye mery analiticheskikh differentsialov”, Nekotorye voprosy teorii priblizhenii, Sb., ed. A. A. Gonchar, IL, M., 1963, 87–100

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

[11] Karateodori K., Konformnoe otobrazhenie, Gostekhizdat, M.–L., 1934

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

[13] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, M.–L., 1950

[14] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976