维伦金-傅里叶级数的特殊德瓦雷-普桑型矩阵变换均值近似法

Pub Date : 2024-09-16 DOI:10.1007/s10476-024-00049-2

I. Blahota, D. Nagy

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引用次数: 0

摘要

我们考虑了基于特殊矩阵的 de la Vallée Poussin 类傅里叶级数均值对 Vilenkin 系统的规范收敛性。我们估算了上面命名的均值与相应函数在规范上的差异，上估算值由函数的连续性模量给出。我们还给出了关于常模和几乎无处不收敛的定理。

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Approximation by a special de la Vallée Poussin type matrix transform mean of Vilenkin–Fourier series

We consider the norm convergence for a special matrix-based de la Vallée Poussin-like mean of Fourier series with respect to the Vilenkin system. We estimate the difference between the named mean above and the corresponding function in norm, and the upper estimation is given by the modulus of continuity of the function. We also give theorems with respect to norm and almost everywhere convergences.

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