Best-possible one-sided approximations in the classes $W_\alpha^rV$ ($r>-1$) by trigonometric polynomials in the metric of $L_1$

V. G. Doronin, A. A. Ligun

Dneprodzerzhinsk Industrial Institute

Abstract: The quantities $\sup\limits_{f\in W_\alpha^rV}\Hat{\Hat E}_n(f)_1$ ($r>-1$, $-\infty<\alpha<\infty$, $n=1,2\dots)$ are calculated, where $\Hat{\Hat E}_n(f)_1$ is the best approximation from above of the function $f$ by trigonometric polynomials of order $\le n-1$ in the metric of $L_1$.

UDC: 517.5

Received: 19.02.1976

 English version: Mathematical Notes, 1977, 22:3, 688–696

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