Literature cited
N. P. Korneichuk, Splines in the Theory of Approximation [in Russian], Nauka, Moscow (1984).
N. P. Korneichuk, Exact Constants in the Theory of Approximation [in Russian], Nauka, Moscow (1987).
S. M. Nikok'skii, “Approximation of functions using trigonometric polynomials in the mean,” Izv. Akad. Nauk SSSR, Ser. Mat.,10, No. 3, 207–256 (1946).
N. P. Korneichuk, Extremal Problems in the Theory of Approximation [in Russian], Nauka, Moscow (1976).
V. K. Dzyadyk, “Best approximation on classes of periodic functions defined by integrals of linear combinations of absolutely monotonous kernels,” Mat. Zametki,16, No. 5, 691–701 (1974).
M. G. Krein, “The theory of best approximation of periodic functions,” Dokl. Akad. Nauk SSSR,18, Nos. 4–5, 245–249 (1938).
A. Pinkus, “On n-widths of periodic functions,” J. Anal. Math.,35, 209–235 (1979).
A. K. Kushpel', “Exact bounds on widths of classes of convolutions,” Izv. Akad. Nauk SSSR, Ser. Mat.,52, No. 6, 1305–1322 (1988).
A. K. Kushpel', “SK-splines and exact estimates of widths of functional classes in the space C2π,” Preprint No. 85.51, Kiev, IM Akad. Nauk UkrSSR (1985).
V. T. Shevaldin, “Lower bounds for widths of classes of sourcewise representable functions,” Trudy MIAN SSSR,189, 185–201 (1989).
E. M. Stein, “Functions of exponential type,” Ann. Math.,65, 582–592 (1957).
Yu. N. Subbotin, “Approximation using ‘spline’ functions and estimates of widths,” Trudy MIAN SSSR,109, 35–60 (1971).
A. K. Kushpel', “Estimates of widths of classes of convolutions in spaces S and L,” Ukr. Mat., Zh.,41, No. 8, 1070–1076 (1989).
Nguyen Tkhi Tkh'eu Khoa, “Operator D(D2 + 1) η ... η (D2 + n2) and trigonometric interpolation,” Anal. Math.,15, No. 4, 291–306 (1989).
L. V. Taikov, “Best approximation in the mean for certain classes of analytic functions,” Mat. Zametki,1, No. 2, 155–162 (1967).
V. T. Shevaldin, Lower Bounds for Widths of Certain Classes of Periodic Functions [in Russian], Preprint, Sverdlovsk, Akad. Nauk SSSR (1989).
J. Alberg, E. Nilson, and J. Walsh, Theory of Splines and Its Applications [Russian translation], Mir, Moscow (1972).
V. M. Tikhomirov, “Widths of sets in functional spaces and theory of best approximations,” Usp. Mat. Nauk,15, No. 3 (93), 81–120 (1960).
V. M. Tikhomirov, “Best methods of approximation and integration of differentiable functions in the space C[−1; 1],” Mat. Sb.,80, No. 2, 290–304 (1969).
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Translated from Matematicheskie Zametki, Vol. 51, No. 6, pp. 126–136, June, 1992.
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Shevaldin, V.T. Widths of classes of convolutions with Poisson kernel. Math Notes 51, 611–617 (1992). https://doi.org/10.1007/BF01263308
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DOI: https://doi.org/10.1007/BF01263308