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This article is cited in 1 scientific paper (total in 1 paper)
On the coefficients of everywhere convergent series in some rearranged orthonormal systems
G. M. Mushegyan
Abstract:
In this paper the author establishes the existence of a series
$\sum a_{\nu_k}\cos\nu_kx+b_{\nu_k}\sin\nu_kx$ in some rearranged trigonometric system, which converges everywhere to a Lebesgue integrable function and whose coefficients $a_{\nu_k}$ and $b_{\nu_k}$, $k=1,2,\dots$, are not the Fourier–Lebesgue coefficients of this function. Similar results are established for the Haar system and some other systems.
Bibliography: 17 titles.
Received: 01.03.1976
Citation:
G. M. Mushegyan, “On the coefficients of everywhere convergent series in some rearranged orthonormal systems”, Izv. Akad. Nauk SSSR Ser. Mat., 42:4 (1978), 807–832; Math. USSR-Izv., 13:1 (1979), 107–132
Linking options:
https://www.mathnet.ru/eng/im1847https://doi.org/10.1070/IM1979v013n01ABEH002014 https://www.mathnet.ru/eng/im/v42/i4/p807
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Abstract page: | 222 | Russian version PDF: | 81 | English version PDF: | 3 | References: | 34 | First page: | 1 |
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