Literature cited
S. M. Nikol'skii, Approximation of Functions of Several Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1977).
S. B. Stechkin, “Best approximation of linear operators,” Mat. Zametki,1, No. 2, 137–148 (1967).
V. V. Arestov, “On best approximation of differentiation operators in uniform metric,” Candidate's Dissertation, Sverdlovsk (1969).
Y. Domar, “An extremal problem related to Kolmogoroff's inequality for bounded functions,” Ark Mat.,7, 434–441 (1968).
A. N. Kolmogorov, “On inequalities between upper bounds of successive derivatives of a function in an infinite interval,” Uch. Zap. Mosk. Gos. Univ., No. 30, Mat.,3, 3–16 (1939).
V. N. Gabushin, “Best approximation of functionals in certain sets,” Mat. Zametki,8, No. 5, 551–562 (1970).
V. V. Arestov, “On best approximation of differentiation operators,” Mat. Zametki,1, No. 2, 149–154 (1967).
Ch. Micchelli, “On an optimal method for the numerical differentiation of smooth functions,” J. Approx. Theory,18, 189–204 (1976).
V. K. Ivanov, V. V. Vasin, and V. P. Tanana, Theory of Linear Ill-Posed Problems and Its Applications [in Russian], Nauka, Moscow (1978).
H. Kallioniemi, “On representation formulas for intermediate derivatives,” Math. Scand.,39, No. 2, 315–326 (1976).
V. N. Konovalov, “Exact inequalities for norms of functions and of third partial, second mixed, or directional, derivatives,” Mat. Zametki,23, No. 1, 67–78 (1978).
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Translated from Matematicheskie Zametki, Vol. 29, No. 5, pp. 731–742, May, 1981.
The author thanks V. M. Tikhomirov for his interest and assistance.
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Buslaev, A.P. Approximation of a differentiation operator. Mathematical Notes of the Academy of Sciences of the USSR 29, 372–378 (1981). https://doi.org/10.1007/BF01158361
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DOI: https://doi.org/10.1007/BF01158361