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On Jackson’s theorem in the space $$\ell_2(\mathbb{Z}_2^n)$$. (English. Russian original) Zbl 0905.41008
Math. Notes 60, No. 3, 288-299 (1996); translation from Mat. Zametki 60, No. 3, 390-405 (1996).
Authors’ summary: Estimates of Jackson’s constants in the space $$\ell_2 (\mathbb{Z}^n_2)$$ are given for the case of approximation by sums of subspaces on which irreducible representations of the isometry group of $$\mathbb{Z}^n_2$$ act and for the case in which the modulus of continuity is defined using generalized translations. Coding theory results on efficiency estimates for binary $$d$$-codes with respect to the Hamming distance are used.
MSC:
 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
Full Text:
References:
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