This article is cited in 13 papers

Approximation of Sobolev Classes by Their Finite-Dimensional Sections

V. N. Konovalov

Institute of Mathematics, Ukrainian National Academy of Sciences

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 in $L_\infty$ or $L_1$ on higher-order derivatives, we present the exact orders of such widths in the spaces $L_q$.

UDC: 517.5

Received: 16.11.2001

DOI: 10.4213/mzm429

 English version: Mathematical Notes, 2002, 72:3, 337–349

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