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Mat. Zametki, 1977, Volume 22, Issue 2, Pages 257–268 (Mi mz8046)  

Upper bounds of best one-sided approximations of the classes $W^rL_\psi$ in the metric of $L$

V. G. Doronina, A. A. Ligunb

a Dnepropetrovsk State University
b Dneprodzerzhinsk Industrial Institute

Abstract: The lowest upper bound is obtained for best one-sided approximations of classes $W^rL_\psi$ ($r=1,2,…$) by trigonometric polynomials and splines of minimum deficiency with equidistant knots, in the metric of space $L$, where $W^rL_\psi=\{f:f(x+2\pi)=f(x)$, $f^{(r-1)}(x)$ is absolutely continuous, $\|f^{(r)}\|_{L_\psi}\le1\}$ and $L_\psi$ is an Orlicz space.

Full text: PDF file (717 kB)

English version:
Mathematical Notes, 1977, 22:2, 633–640

Bibliographic databases:

UDC: 517.5
Received: 30.12.1975

Citation: V. G. Doronin, A. A. Ligun, “Upper bounds of best one-sided approximations of the classes $W^rL_\psi$ in the metric of $L$”, Mat. Zametki, 22:2 (1977), 257–268; Math. Notes, 22:2 (1977), 633–640

Citation in format AMSBIB
\Bibitem{DorLig77}
\by V.~G.~Doronin, A.~A.~Ligun
\paper Upper bounds of best one-sided approximations of the classes $W^rL_\psi$ in the metric of~$L$
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 2
\pages 257--268
\mathnet{http://mi.mathnet.ru/mz8046}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=481759}
\zmath{https://zbmath.org/?q=an:0365.42001}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 2
\pages 633--640
\crossref{https://doi.org/10.1007/BF01780973}


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