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Mat. Zametki, 1969, Volume 6, Issue 5, Pages 567–572 (Mi mz6964)  

On sequences of Fourier coefficients of functions of Hölder classes

G. S. Abros'kinaa, B. S. Mityaginb

a Voronezh State Pedagogical Institute
b Central Economics and Mathematics Institute, USSR Academy of Sciences

Abstract: The following theorem is proved. Let $\{\psi_l(t)\}$ be an arbitrary complete orthonormal system on $[0,1]$ and let $1/2<\alpha<1$. Then an $f(t)\in C_\beta$ exists for all $\beta<\alpha$ such that $\sum_{k=1}^\infty|c_k(f)|^p=\infty$, $p=2/(1+2\alpha)$, where $c_k(f)=\int\limits_0^1f\psi_k dt$.

Full text: PDF file (348 kB)

English version:
Mathematical Notes, 1969, 6:5, 800–803

Bibliographic databases:

UDC: 517.5
Received: 17.12.1968

Citation: G. S. Abros'kina, B. S. Mityagin, “On sequences of Fourier coefficients of functions of Hölder classes”, Mat. Zametki, 6:5 (1969), 567–572; Math. Notes, 6:5 (1969), 800–803

Citation in format AMSBIB
\Bibitem{AbrMit69}
\by G.~S.~Abros'kina, B.~S.~Mityagin
\paper On sequences of Fourier coefficients of functions of H\"older classes
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 5
\pages 567--572
\mathnet{http://mi.mathnet.ru/mz6964}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=306791}
\zmath{https://zbmath.org/?q=an:0191.36703|0186.12202}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 5
\pages 800--803
\crossref{https://doi.org/10.1007/BF01101407}


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