Geodesic
Constructive description of certain classes of functions on quasismooth arcs
Izvestiya. Mathematics, Tome 44 (1995) no. 1, pp. 193-206 
V. V. Andrievskii; V. V. Maimeskul. Constructive description of certain classes of functions on quasismooth arcs. Izvestiya. Mathematics, Tome 44 (1995) no. 1, pp. 193-206. http://geodesic.mathdoc.fr/item/IM2_1995_44_1_a9/
@article{IM2_1995_44_1_a9,
     author = {V. V. Andrievskii and V. V. Maimeskul},
     title = {Constructive description of certain classes of functions on quasismooth arcs},
     journal = {Izvestiya. Mathematics},
     pages = {193--206},
     year = {1995},
     volume = {44},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_44_1_a9/}
}
TY  - JOUR
AU  - V. V. Andrievskii
AU  - V. V. Maimeskul
TI  - Constructive description of certain classes of functions on quasismooth arcs
JO  - Izvestiya. Mathematics
PY  - 1995
SP  - 193
EP  - 206
VL  - 44
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_1995_44_1_a9/
LA  - en
ID  - IM2_1995_44_1_a9
ER  - 
%0 Journal Article
%A V. V. Andrievskii
%A V. V. Maimeskul
%T Constructive description of certain classes of functions on quasismooth arcs
%J Izvestiya. Mathematics
%D 1995
%P 193-206
%V 44
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_1995_44_1_a9/
%G en
%F IM2_1995_44_1_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

Three classes of functions are introduced, corresponding to known results in the theory of uniform polynomial approximation of functions on arcs in the complex plane. The structural properties of functions in these classes are described from a unified point of view, which allows one to understand more fully their nature and the differences between them.

[1] D. J. Newman, “Jackson's theorem oh complex arcs”, J. Approx. Theory, 10:3 (1974), 206–217 | DOI | MR | Zbl

[2] F. D. Lesley, “Best approximation on smooth arcs”, J. Approx. Theory, 18:4 (1976), 378–382 | DOI | MR | Zbl

[3] V. K. Dzyadyk, Vvedenie v teoriyu ravnomernogo priblizheniya funktsii polinomami, Nauka, M, 1977 | MR | Zbl

[4] V. V. Andrievskii, “Pryamye teoremy priblizheniya na kvazikonformnykh dugakh”, Izv. AN SSSR. Ser. matem., 44:2 (1980), 243–261 | MR | Zbl

[5] Dzh. I. Mamedkhanov, “Voprosy nailuchshei polinomialnoi approksimatsii v kompleksnoi ploskosti”, Teoriya funktsii i priblizhenii, Tr. Saratov. zim. shk., Saratov. un-t, 1983, 149–156 | MR

[6] J. M. Anderson, A. Hinkkanen, F. D. Lesley, “On theorems of Jackson and Bernstein type in the complex plane”, Constr. Approx., 4:3 (1988), 307–321 | DOI | MR

[7] E. M. Dynkin, “O ravnomernom priblizhenii funktsii v zhordanovykh oblastyakh”, Sib. matem. zhurn., 18:4 (1977), 775–786 | MR

[8] E. M. Dynkin, “Konstruktivnaya kharakteristika funktsii klassov S. L. Soboleva i O. V. Besova”, Tr. MIAN, 155, 1981, 41–76 | MR | Zbl

[9] V. V. Maimeskul, “O $J$-svoistve zhordanovykh dug”, Ukr. matem. zhurn., 40:5 (1988), 647–649 | MR | Zbl

[10] M. A. Lavrentev, “O nekotorykh granichnykh zadachakh v teorii odnolistnykh funktsii”, Matem. sb., 1(43) (1936), 815–846 | MR

[11] V. V. Andrievskii, “Nekotorye svoistva kontinuumov s kusochno-kvazikonformnoi granitsei”, Ukr. matem. zhurn., 32:4 (1980), 435–440 | MR | Zbl

[12] V. V. Andrievskii, “Approksimatsionnaya kharakteristika klassov funktsii na kontinuumakh kompleksnoi ploskosti”, Matem. sb., 125(167):1(9) (1984), 70–88 | MR

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

[14] N. A. Lebedev, P. M. Tamrazov, “Obratnye teoremy priblizheniya na regulyarnykh kompaktakh kompleksnoi ploskosti”, Izv. AN SSSR. Ser. matem., 34:6 (1970), 1340–1390 | MR | Zbl

[15] P. M. Tamrazov, Gladkosti i polinomialnye priblizheniya, Nauk. dumka, Kiev, 1975 | MR | Zbl