On best and optimal quadrature formulas on classes of bounded analytic functions
Izvestiya. Mathematics, Tome 32 (1989) no. 1, pp. 77-97 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The best quadrature formula is constructed for the Chebyshev weight function and Chebyshev knots, for the class of functions that are analytic in an ellipse with foci at the points $pm1$ and sum of semiaxes $c$, and have their moduli bounded by unity there. Bibliography: 15 titles.
@article{IM2_1989_32_1_a4,
     author = {K. Yu. Osipenko},
     title = {On~best and optimal quadrature formulas on~classes of bounded analytic functions},
     journal = {Izvestiya. Mathematics},
     pages = {77--97},
     year = {1989},
     volume = {32},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1989_32_1_a4/}
}
TY  - JOUR
AU  - K. Yu. Osipenko
TI  - On best and optimal quadrature formulas on classes of bounded analytic functions
JO  - Izvestiya. Mathematics
PY  - 1989
SP  - 77
EP  - 97
VL  - 32
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_1989_32_1_a4/
LA  - en
ID  - IM2_1989_32_1_a4
ER  - 
%0 Journal Article
%A K. Yu. Osipenko
%T On best and optimal quadrature formulas on classes of bounded analytic functions
%J Izvestiya. Mathematics
%D 1989
%P 77-97
%V 32
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_1989_32_1_a4/
%G en
%F IM2_1989_32_1_a4
K. Yu. Osipenko. On best and optimal quadrature formulas on classes of bounded analytic functions. Izvestiya. Mathematics, Tome 32 (1989) no. 1, pp. 77-97. http://geodesic.mathdoc.fr/item/IM2_1989_32_1_a4/

[1] Osipenko K. Yu., “Nailuchshee priblizhenie analiticheskikh funktsii po informatsii ob ikh znacheniyakh v konechnom chisle tochek”, Matem. zametki, 19:1 (1976), 29–40 | MR | Zbl

[2] Bakhvalov N. S., “Ob optimalnoi skorosti integrirovaniya analiticheskikh funktsii”, Zhurn. vychisl. matem. i matem. fiz., 7:5 (1967), 1011–1020 | Zbl

[3] Loeb H. L., “A note on optimal integration in $H_\infty$”, C.R. Acad. Bulgare Sci., 27:5 (1974), 615–619 | MR

[4] Bojanov B. D., “On the existence of optimal quadrature formulae for smooth functions”, Calcolo, 16:1 (1979), 61–70 | DOI | MR | Zbl

[5] Andersson J.-E., Bojanov B. D., “A note on the optimal quadrature in $H_p$”, Numer. Math., 44:2 (1984), 301–308 | DOI | MR | Zbl

[6] Osipenko K. Yu., “Nailuchshie metody priblizheniya analiticheskikh funktsii, zadannykh s pogreshnostyu”, Matem. sb., 118(160) (1982), 350–370 | MR | Zbl

[7] Micchelli C. A., Rivlin T. J., “A survey of optimal recovery”, Optimal estimation in approximation theory, Plenum Press, N.Y., 1977, 1–54 | MR

[8] Rivlin T. J., “The optimal recovery of functions”, Contemp. Math., 9 (1982), 121–151 | MR | Zbl

[9] Osipenko K. Yu., “Optimalnaya interpolyatsiya analiticheskikh funktsii”, Matem. zametki, 12:4 (1972), 465–476 | MR | Zbl

[10] Bojanov B. D., “Best quadrature formula for a certain class of analytic functions”, Zastos. Math., 14 (1974), 441–447 | MR | Zbl

[11] Akhiezer N. I., Elementy teorii ellipticheskikh funktsii, Nauka, M., 1970 | MR | Zbl

[12] Zhuravskii A. I., Spravochnik po ellipticheskim funktsiyam, AN SSSR, M., 1941

[13] Fisher S. D., Micchelli C. A., “The $n$-widths of sets of analytic functions”, Duke Math. J., 47:4 (1980), 789–801 | DOI | MR | Zbl

[14] Gantmakher F. R., Teoriya matrits, Nauka, M., 1967 | MR

[15] Bojanov B. D., “Extremal problems in a set of polynomials with fixed multiplicities of zeros”, C.R. Acad. Bulgare Sci., 31:4 (1978), 377–380 | MR