关于乘法系统和广义导数的数列积分性

Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika Pub Date : 2024-04-08 DOI:10.26907/0021-3446-2024-3-3-14

N. Agafonova, S. Volosivets

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引用次数: 0

摘要

我们给出了关于乘法系统和相应傅里叶级数的级数和的广义导数收敛的一些必要和充分条件。这些条件与 S. Sheng、W.O. Bray 和 C\v .V. Stanojevi´c 的三角函数结果相对应，并扩展了 F. M´oricz 为沃尔什-傅里叶级数证明的一些结果。

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Integrability of series with respect to multiplicative systems and generalized derivatives

We give some necessary and sufficient conditions for the convergence of generalized derivatives of sums of series with respect to multiplicative systems and the corresponding Fourier series. These conditions are counterparts of trigonometric results of S. Sheng, W.O. Bray and C\v .V. Stanojevi´c and extend some results of F. M´oricz proved for Walsh–Fourier series

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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika

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