Estimates of the best bilinear approximations of functions of two
Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 95-109 Cet article a éte moissonné depuis la source Math-Net.Ru

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The orders of the upper bounds over certain classes of functions of two variables for approximations of these functions by sums of products of functions of the individual variables are obtained. As a corollary, optimal estimates are obtained for the singular numbers of integral operators and the Kolmogorov widths of classes of functions having an integral representation with kernels from the classes under consideration. Bibliography: 20 titles.
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     title = {Estimates of the best bilinear approximations of functions of two},
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V. N. Temlyakov. Estimates of the best bilinear approximations of functions of two. Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 95-109. http://geodesic.mathdoc.fr/item/SM_1989_62_1_a5/

[1] Nikolskii S. M., “Funktsii s dominiruyuschei smeshannoi proizvodnoi, udovletvoryayuschei kratnomu usloviyu Gëldera”, Sib. matem. zhurn., 4:6 (1963), 1342–1364

[2] Temlyakov V. N., “Priblizhenie funktsii s ogranichennoi smeshannoi raznostyu trigonometricheskimi polinomami i poperechniki nekotorykh klassov funktsii”, Izv. AN SSSR. Ser. matem., 46 (1982), 171–186 | MR | Zbl

[3] Temlyakov V. N., “O nailuchshikh bilineinykh priblizheniyakh periodicheskikh funktsii mnogikh peremennykh”, DAN SSSR, 286:2 (1986), 301–304 | MR | Zbl

[4] Temlyakov V. N., “Priblizhenie funktsii s ogranichennoi smeshannoi proizvodnoi”, Tr. MIAN, 178, 1986, 3–113 | MR | Zbl

[5] Zigmund A., Trigonometricheskie ryady, Mir, M., 1965 | MR

[6] Uninskii A. P., Neravenstva v smeshannoi norme dlya trigonometricheskikh polinomov i tselykh funktsii konechnoi stepeni, Materialy Vsesoyuzn. simpoziuma po teoremam vlozheniya, no. 1966, Baku | Zbl

[7] Kashin B. S., “Poperechniki nekotorykh konechnomernykh mnozhestv i klassov gladkikh funktsii”, Izv. AN SSSR. Ser. matem., 41 (1977), 334–351 | Zbl

[8] Gluskin E. D., Garnaev A. Yu., “O poperechnikakh evklidova shara”, DAN SSSR, 277:5 (1984), 1048–1052 | MR | Zbl

[9] Gluskin E. D., “Normy sluchainykh matrits i poperechniki konechnomernykh mnozhestv”, Matem. sb., 120(162) (1983), 180–189 | MR | Zbl

[10] Kakhan Zh.-P., Absolyutno skhodyaschiesya ryady Fure, Mir, M., 1976

[11] Kashin B. S., “O poperechnikakh klassov Soboleva maloi gladkosti”, Vestn. MGU. Ser. 1. Matem., mekh., 1981, no. 5, 50–54 | MR | Zbl

[12] Schmidt E., “Zur Theorie der linearen und michtlinearen Integralgeichungen”, Math. Ann., 63 (1907), 433–476 | DOI | MR | Zbl

[13] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov, Nauka, M., 1965

[14] Birman M. Sh., Solomyak M. Z., “Otsenki singulyarnykh chisel integralnykh operatorov”, UMN, 32:1 (1977), 17–84 | MR | Zbl

[15] Smithies F., “The eigen-values and singular values of integral equations”, Proc. London Math. Soc. (2), 43 (1937), 255–279 | DOI | Zbl

[16] Cochran J. A., “Summability of singular values of $L^2$ kernels. Analogies with Fourier series”, Enseigment Math., 22:1–2 (1976), 141–157 | MR | Zbl

[17] Pich A., “Sobstvennye chisla integralnykh operatorov”, DAN SSSR, 247:6 (1979), 1324–1327 | MR

[18] Pietsch A., “Eigenvalues of integral operators, P. I”, Math. Ann., 247 (1980), 169–178 | DOI | MR | Zbl

[19] Birman M. Sh., Solomyak M. Z., “Ob otsenkakh singulyarnykh chisel integralnykh operatorov. II”, Vestn. LGU, 1967, no. 13, 21–28 | MR | Zbl

[20] Kashin B. S., Saakyan A. A., Ortogonalnye ryady, Nauka, M., 1984 | MR | Zbl