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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
Received: 26.01.1973

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}


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