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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1977, Volume 22, Issue 5, Pages 671–678 (Mi mz8091)

Diameters of a class of smooth functions in the space $L_2$

R. S. Ismagilova, Kh. Nasyrova

a Moscow Institute of Electronic Engineering

Abstract: The class $V_\psi$, consisting of the smooth functions $f(t)$, $0\le t\le1$, satisfying the condition $\int_0^1\psi[f^{(r)}(t)] dt\le1$, where the function $\psi(t)$ is nonnegative and $r$ is a natural number, is studied. Under certain restrictions on the function $\psi(t)$ ensuring the compactness of the class $V_\psi$, the order of decrease of the Kolmogorov diameters $d_n(V_\psi)$ is computed. The analogous problem for the case $r=1$ is solved also for functions of several variables.

Full text: PDF file (494 kB)

English version:
Mathematical Notes, 1977, 22:5, 865–870

Bibliographic databases:

UDC: 517

Citation: R. S. Ismagilov, Kh. Nasyrova, “Diameters of a class of smooth functions in the space $L_2$”, Mat. Zametki, 22:5 (1977), 671–678; Math. Notes, 22:5 (1977), 865–870

Citation in format AMSBIB
\Bibitem{IsmNas77}
\by R.~S.~Ismagilov, Kh.~Nasyrova
\paper Diameters of a~class of smooth functions in the space $L_2$
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 5
\pages 671--678
\mathnet{http://mi.mathnet.ru/mz8091}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=473653}
\zmath{https://zbmath.org/?q=an:0372.41013}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 5
\pages 865--870
\crossref{https://doi.org/10.1007/BF01098351}