Abstract
For any ε>O there is constructed a finitary function
of one variable, of finite smoothness inR 1, with a support containing zero, satisfying the condition
whereQ(x) is any polynomial of degree no higher thann, and, moreover, such that
.
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Literature cited
K. K. Golovkin, “On the approximation of functions in arbitrary norms,” Tr. Mat. Inst. Steklova,70, 26–37 (1964).
S. G. Mikhlin, “On constant multipliers in error bounds of variation-net approximation,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,80, 125–166 (1978).
V. P. Il'in, “On the approximation of functions of class B Zp,θ (G) by anisotopic means,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,80, 30–47 (1978).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 90, pp. 265–267, 1979.
The author thanks V. P. Il'in for posing the problem and for attention to the work.
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Shubochkina, T.A. Averaging kernels with small norms. J Math Sci 20, 2096–2098 (1982). https://doi.org/10.1007/BF01680573
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DOI: https://doi.org/10.1007/BF01680573