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On the problem of linear widths of the classes \(B_{p,\theta}^r\) of periodic functions of many variables. (English. Ukrainian original) Zbl 1309.41014

Ukr. Math. J. 66, No. 7, 1085-1098 (2014); translation from Ukr. Mat. Zh. 66, No. 7, 970-982 (2014).
Summary: We establish order estimates for the linear widths of the classes \(B_{p,\theta}^r\) of periodic functions of many variables in the space \(L_q\) for some relationships between the parameters \(p,q\), and \(\theta\).

MSC:

41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
42A10 Trigonometric approximation
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