Sharp estimates of the widths of convolution classes
Izvestiya. Mathematics , Tome 33 (1989) no. 3, pp. 631-649.

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On the basis of an apparatus that is a generalization of polynomial splines, sharp estimates of the widths of convolution classes are found. Bibliography: 39 titles.
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A. K. Kushpel'. Sharp estimates of the widths of convolution classes. Izvestiya. Mathematics , Tome 33 (1989) no. 3, pp. 631-649. http://geodesic.mathdoc.fr/item/IM2_1989_33_3_a8/

[1] Kolmogorov A. N., “Über die besste Annaherung von Functionen einer gegebenen Functionklassen”, Ann. of Math., 37 (1936), 107–110 | DOI | MR | Zbl

[2] Tikhomirov V. M., “Poperechniki mnozhestv v funktsionalnykh prostranstvakh i teoriya priblizheniya”, Uspekhi matem. nauk, 15:3 (1960), 81–120 | MR | Zbl

[3] Tikhomirov V. M., “Nailuchshie metody priblizheniya i interpolirovaniya v prostranstve $C[-1,1]$”, Matem. sb., 80:2 (1969), 290–304 | Zbl

[4] Tikhomirov V. M., Nekotorye voprosy teorii priblizhenii, MGU, M., 1976, 304 pp. | MR

[5] Miccelli C. A., Pinkus A., “On $n$-widths in $L^\infty$”, Trans. Amer. Math. Soc., 234 (1977), 139–174 | DOI | MR

[6] Pinkus A., “On $n$-widths of periodic functions”, J. d'analyse Mathematique, 35 (1979), 209–235 | DOI | MR | Zbl

[7] Karlin S., Total positivity, v. I, Stanford Univ. Press, 1968, 576 pp. | MR

[8] Hirshman I. I., Widder D. V., The convolution Transform, Princeton University Press, 1955, 84–107 | MR

[9] Mairhuber J. C., Shoenberg I. J., Williamson R. E., “On variation diminising transformations on the circle”, Rend. Circ. Mathem. Palermo, Ser. II, VIII (1959), 241–270 | DOI | MR

[10] Chui C. K. Smith P. W., “Some nonlinear approximation problems related to $N$ widths”, J. Approx. Theory, 13:4 (1975), 421–430 | DOI | MR | Zbl

[11] Micchelli C. A., Pinkus A., “Total Positivity and the exact $n$-widths of certain sets in $L_1$”, Pacific J. Math., 71:2 (1977), 499–515 | MR

[12] Shevaldin V. T., “$\mathscr{L}$-splainy i poperechniki”, Matem. zametki, 33:5 (1983), 735–744 | MR | Zbl

[13] Kushpel A. K., $sk$-splainy i tochnye otsenki poperechnikov funktsionalnykh klassov v prostranstve $C_{2\pi}$, Preprint No 85.51, In-t matematiki AN USSR, Kiev, 1985 | MR

[14] Kushpel A. K., Ekstremalnye svoistva splainov i poperechniki klassov periodicheskikh funktsii v prostranstve $C_{2\pi}$, Preprint No 84.25, In-t matematiki AN USSR, Kiev, 1984 | MR

[15] Kushpel A. K., “Ob interpolyatsii periodicheskikh funktsii”, Uspekhi matem. nauk, 1986, no. 1, 114–116 | MR | Zbl

[16] Kushpel A. K., “Poperechniki klassov periodicheskikh funktsii v prostranstve $C_{2\pi}$”, Issledovaniya po teoreticheskim i prikladnym voprosam matematiki, In-t matematiki AN USSR, Kiev, 1986, 26 | MR

[17] Subbotin Yu. N., “O kusochno-polinomialnoi interpolyatsii”, Matem. zametki, 1:1 (1967), 63–70 | MR | Zbl

[18] Ahlberg J. H., Nilson E. N., Walsch J. L., “Best approximation and convergence properties of higher-order spline approximations”, J. Math. and Mech., 14:2 (1965), 231–243 | MR | Zbl

[19] Walsch J. L., Ahlberg J. H., Nilson E. N., “Best approximations and convergence properties of higher-order spline fits (abstract)”, Notices Amer. Soc. Math., 10:2 (1963), 202

[20] Ahlberg J. H., Nilson E. N., “Convergence properties of spline fit”, J. Soc. Ind. Appl. Math., 11:1 (1963), 95–104 | DOI | MR | Zbl

[21] Walsch J. L., Ahlberg J. H., Nilson E. N., “Best approximation properties of spline fit”, J. Math. and Mech., 11:2 (1962), 225–234 | MR

[22] Galkin P. V., “O razreshimosti zadachi periodicheskoi splain-interpolyatsii”, Matem. zametki, 8:5 (1970), 563–573 | MR | Zbl

[23] Zhensykbaev A. A., Nekotorye voprosy priblizheniya splainami v funktsionalnykh prostranstvakh, Dis. $\dots$ kand. fiz.-matem. nauk, Dnepropetrovsk, 1973 | Zbl

[24] Korneichuk N. P., Splainy v teorii priblizheniya, Nauka, M., 1984 | MR

[25] Birkhoff G., de Boor Carl, “Error bounds for spline interpolation”, J. Math. and Mech., 13:5 (1964), 827–835 | MR | Zbl

[26] Sard A., Linear approximation, Math. Surveys, 9, Am. Math. Soc., Providence, 1963 | MR | Zbl

[27] Alberg Dzh., Nilson E., Uolsh Dzh., Teoriya splainov i ee prilozheniya, Mir, M., 1972, 316 pp. | MR | Zbl

[28] Shevaldin V. T., “Interpolyatsionnye periodicheskie $\mathscr{L}$-splainy s ravnomernymi uzlami”, Priblizhenie polinomami i splainami, Sverdlovsk, 1985, 140–147 | MR | Zbl

[29] Lankaster P., Teoriya matrits, Nauka, M., 1978, 245 pp. | MR

[30] Golomb M., “Approximation by periodic spline interpolations on uniform meshens”, J. Approx. Theory, 1 (1968), 26–65 | DOI | MR | Zbl

[31] Gorbachuk V. I., Gorbachuk M. L., “Trigonometricheskie ryady i obobschennye periodicheskie funktsii”, Dokl. AN SSSR, 257:4 (1981), 799–804 | MR

[32] Edvardc R., Ryady Fure v sovremennom izlozhenii, Mir, M., 1985

[33] Stepanets A. I., “Klassifikatsiya periodicheskikh funktsii i skorost skhodimosti ryadov Fure”, Izv. AN SSSR. Ser. matem., 50:1 (1986), 101–136 | MR

[34] Korneichuk N. Ya., Ekstremalnye zadachi teorii priblizheniya funktsii, Nauka, M., 1976, 320 pp. | MR

[35] Nady Sz. B., “Über gewisse Extremolfragen bei transformierten trigonometrischen Entwickhmgen”, Berichte Akad. d. Wiss, 90, Leipzig, 1938, 103–134

[36] Timan A. F., Teoriya priblizhenii funktsii deistvitelnogo peremennogo, Fizmatgiz, M., 1960, 624 pp.

[37] Favard J., “Sur l'approximation des fonctions periodiques par des polynomes trigonometriques”, C.R. Acad. Sci., 203 (1936), 1122–1124 | Zbl

[38] Akhiezer N. I., Krein M. G., “O nailuchshem priblizhenii trigonometricheskimi summami differentsiruemykh periodicheskikh funktsii”, Dokl. AN SSSR, 15:3 (1937), 107–115

[39] Krein M. G., “K teorii nailuchshego priblizheniya periodicheskikh funktsii”, Dokl. AN SSSR, 18:4,5 (1938), 245–249 | Zbl