Abstract
We consider relative widths characterizing the best approximation of a fixed set by its sections of given dimension. For Sobolev classes of periodic functions of a single variable with constraints inL ∞ orL 1 on higher-order derivatives, we present the exact orders of such widths in the spaces L q.
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Konovalov, V.N. Approximation of Sobolev Classes by Their Finite-Dimensional Sections. Mathematical Notes 72, 337–349 (2002). https://doi.org/10.1023/A:1020547320561
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DOI: https://doi.org/10.1023/A:1020547320561