On the complexity of the approximate table representation of discrete analogs of functions of finite smoothness in the metric of $L^p$

G. G. Amanzhaev

M. V. Lomonosov Moscow State University

Abstract: For discrete analogs of classes of functions of finite smoothness, we study the quantity $\log\operatorname{Approx}$ characterizing the minimal necessary length of tables that allow us to reconstruct functions from these classes with error not exceeding 1 in the metric of the space $L^p$.

UDC: 517.5+519.7

Received: 04.02.1997

DOI: 10.4213/mzm1440

 English version: Mathematical Notes, 1998, 64:5, 557–561

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