Abstract
We present sufficient conditions for kernels to belong to the classN *n . In certain cases, this enables us to find exact values of the best approximations of classes of convolutions by trigonometric polynomials in the metrics ofC andL.
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References
A. I. Stepanets,Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).
M. G. Krein, “To the theory of the best approximation of periodic functions,”Dokl. Akad. Nauk SSSR,18, No. 4–5, 245–249 (1938).
V. T. Shevaldin, “Widths of classes of convolutions with Poisson kernels,”Mat. Zametki,51, No. 6, 126–136 (1992).
N. P. Korneichuk,Exact Constants in Approximation Theory [in Russian], Nauka, Moscow (1987).
V. F. Babenko, “Approximation of classes of convolutions,”Sib. Mat. Zh.,28, No. 5, 6–21 (1987).
S. M. Nikol'skii, “Approximations of functions by trigonometric polynomials in the mean,”Izv. Akad. Nauk SSSR, Ser. Mat.,10, No. 3, 207–256 (1946).
V. K. Dzyadyk, “On the best approximation on classes of periodic functions defined by integrals of a linear combination of absolutely monotone kernels,”Mat. Zametki,16, No. 5, 691–701 (1974).
Nguen Thi Thieu Hoa, “The operatorD(D 2 + 1 2) (D2+22)...(D 2 +n 2) and trigonometric interpolation,”Anal. Math.,15, No. 4, 291–306 (1989).
B. Nagy, Über gewisse Extremolfragen bei transformierten trigonometrishen Entwicklungen,”Berichte Akad. Wiss. Leipzig,90, 103–134 (1938).
A. I. Stepanets and A. S. Serdyuk, “Lower bounds for widths of classes of convolutions of periodic functions in the metrics ofC andL,”Ukr. Mat. Zh.,49, No. 8, 1112–1122 (1995).
A. K. Kushpel', “Exact estimates of widths of classes of convolutions,”Izv. Akad. Nauk SSSR, Ser. Mat.,52, No. 6, 1305–1322 (1988).
A. Pinkus, “On n-widths of periodic functions,”J. Anal. Math.,35, 209–235 (1979).
J. C. Mairhuber, I. J. Schoenberg, and Williamson, “On variation diminishing transformations on the circle,”Rend. Circ. Math. Palermo. Serie II. Jomo VIII. Anno, 241–270 (1959).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 9, pp. 1261–1265, September, 1995.
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Serdyuk, A.S. On the best approximation of classes of convolutions of periodic functions by trigonometric polynomials. Ukr Math J 47, 1435–1440 (1995). https://doi.org/10.1007/BF01057518
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DOI: https://doi.org/10.1007/BF01057518