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Matematicheskie Zametki, 1969, Volume 6, Issue 5, Pages 567–572
(Mi mzm6964)
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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 $c_k(f)=\int\limits_0^1f\psi_k\,dt$.
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
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https://www.mathnet.ru/eng/mzm6964 https://www.mathnet.ru/eng/mzm/v6/i5/p567
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Abstract page: | 283 | Full-text PDF : | 128 | First page: | 1 |
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