On Whitney's theorem and constants
Sbornik. Mathematics, Tome 81 (1995) no. 2, pp. 281-295 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is proved that the Whitney constants are bounded by 2.
@article{SM_1995_81_2_a1,
     author = {Yu. V. Kryakin},
     title = {On {Whitney's} theorem and constants},
     journal = {Sbornik. Mathematics},
     pages = {281--295},
     year = {1995},
     volume = {81},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_81_2_a1/}
}
TY  - JOUR
AU  - Yu. V. Kryakin
TI  - On Whitney's theorem and constants
JO  - Sbornik. Mathematics
PY  - 1995
SP  - 281
EP  - 295
VL  - 81
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1995_81_2_a1/
LA  - en
ID  - SM_1995_81_2_a1
ER  - 
%0 Journal Article
%A Yu. V. Kryakin
%T On Whitney's theorem and constants
%J Sbornik. Mathematics
%D 1995
%P 281-295
%V 81
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1995_81_2_a1/
%G en
%F SM_1995_81_2_a1
Yu. V. Kryakin. On Whitney's theorem and constants. Sbornik. Mathematics, Tome 81 (1995) no. 2, pp. 281-295. http://geodesic.mathdoc.fr/item/SM_1995_81_2_a1/

[1] Whitney H., “On functions with bounded $n$-th differences”, J. Math. Pure et Appl., 36 (1957), 67–95 | MR | Zbl

[2] Burkill H., “Cesaro–Perron absolute periodic functions”, Proc. London Math. Soc., 3 (1952), 150–174 | DOI | MR

[3] Brudnyi Yu. A., Issledovaniya po teorii lokalnykh priblizhenii, Diss. ...doktora fiz.-matem. nauk, Yaroslavl, 1977

[4] Storozhenko E. A., Priblizhenie funktsii i teoremy vlozheniya v $L^p$ i $H^p$, Diss. ...doktora fiz.-matem. nauk, Tbilisi, 1979

[5] Osvald P., “Priblizhenie splainami v metrike $L_p$, $0

1$”, Math. Nachr., 94 (1984), 69–96 | MR

[6] Sendov B., “On the constants of H. Whitney”, C. R. Acad. Bul. Sci., 35 (1982), 431–434 | MR | Zbl

[7] Ivanov K., Takev M., “$O(n\ln (n))$ bounds of constants of H. Whitney”, C. R. Acad. Bul. Sci., 38:9 (1985), 1129–1131 | MR | Zbl

[8] Binev P., “$O(n)$ bounds of Whitney constants”, C. R. Acad. Bul. Sci., 38:10 (1985), 1315–1317 | MR

[9] Sendov B., “The constants of H. Whitney are bounded”, C. R. Acad. Bul. Sci., 38:10 (1985), 1299–1302 | MR | Zbl

[10] Sendov B., “Ob odnoi teoreme Kh. Uitni”, DAN SSSR, 291 (1986), 1296–1300 | MR | Zbl

[11] Kryakin Yu. V., “O konstantakh Uitni”, Matem. zametki, 46:2 (1989), 155–157 | MR | Zbl

[12] Brudnyi Yu. A., “Konstanty Uitni”, Sovremennye problemy teorii funktsii, Tez. dokl. Vsesoyuz. Shkoly–konferentsii (19–29 maya 1989), Baku | Zbl

[13] Sendov B., Popov V., The average moduli of smoothness, J. Wiley Sons, 1989 | MR

[14] Kryakin Yu. V., Kovalenko L. G., “O konstantakh Uitni v klassakh $L_p$”, Izv. vuzov. Matematika, 1992, no. 1, 69–77 | MR | Zbl

[15] Kryakin Yu., “On the constant of H.Whitney in $L^p$, $1 \le p \le \infty $”, Math. Balk., 4:4 (1990), 158–174 | MR

[16] Kryakin Yu. V., “O tochnykh konstantakh v teoreme Uitni”, Matem. zametki, 54:1 (1993), 34–51 | MR | Zbl

[17] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady, Nauka, M., 1981 | MR | Zbl

[18] Malozemov V. N., “Ob otklonenii lomanykh”, Vestn. LGU. Matematika. Mekhanika. Astronomiya, 7:2 (1966), 150–153

[19] Zhuk V. V., Natanson G. I., “K teorii kubicheskikh periodicheskikh splainov po ravnootstoyaschim uzlam”, Vestn. LGU. Matematika. Mekhanika. Astronomiya, 1984, no. 1, 5–11 | MR