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 Mat. Zametki, 1973, Volume 14, Issue 5, Pages 633–644 (Mi mz9948)

The convergence of Fourier series with respect to systems of polynomial kind

A. S. Zinov'ev

Kharkov Aviation Institute

Abstract: We establish sufficient conditions for the convergence of the Fourier expansions of functions from $L_\mu^p$ ($p\geqslant1$) in terms of the order of growth of the system $\{\varphi_n(t)\}$, of polynomial kind, orthonormal with respect to the measure $\mu(t)$ on $[a, b]$ and containing a constant. The convergence is considered either in a given point of the orthogonality interval or inside the interval $[c,d]\subset[a,b]$. In connection with this we obtain estimates for the Lebesgue functions of the system $\{\varphi_n(t)\}$, and we consider the localization problem of the convergence conditions.

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English version:
Mathematical Notes, 1973, 14:5, 923–929

Bibliographic databases:

UDC: 517.5

Citation: A. S. Zinov'ev, “The convergence of Fourier series with respect to systems of polynomial kind”, Mat. Zametki, 14:5 (1973), 633–644; Math. Notes, 14:5 (1973), 923–929

Citation in format AMSBIB
\Bibitem{Zin73} \by A.~S.~Zinov'ev \paper The convergence of Fourier series with respect to systems of polynomial kind \jour Mat. Zametki \yr 1973 \vol 14 \issue 5 \pages 633--644 \mathnet{http://mi.mathnet.ru/mz9948} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=336214} \zmath{https://zbmath.org/?q=an:0296.42012} \transl \jour Math. Notes \yr 1973 \vol 14 \issue 5 \pages 923--929 \crossref{https://doi.org/10.1007/BF01462251}