Abstract
We find the exact values of the n-widths for the classes of periodic differentiable functions in L 2[0, 2π] satisfying the constraint
where h > 0, m ∈ ℕ, r ∈ ℤ+, \(\tilde \Omega _m \)(f (r); t) is the generalized mth order continuity modulus of the derivative f (r) ∈ L 2[0, 2π], while Φ(t) is an arbitrary increasing function such that Φ(0) = 0.
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Original Russian Text Copyright © 2011 Shabozov M. Sh. and Yusupov G. A.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 6, pp. 1414–1427, November–December, 2011.
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Shabozov, M.S., Yusupov, G.A. Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in L 2 . Sib Math J 52, 1124–1136 (2011). https://doi.org/10.1134/S0037446611060176
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DOI: https://doi.org/10.1134/S0037446611060176