On the growth rate of arbitrary sequences of double rectangular Fourier sums (Q643829)
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scientific article; zbMATH DE number 5966625
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the growth rate of arbitrary sequences of double rectangular Fourier sums |
scientific article; zbMATH DE number 5966625 |
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On the growth rate of arbitrary sequences of double rectangular Fourier sums (English)
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2 November 2011
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This paper proves a theorem, which says that let \(\{m_k\}\) and \(\{n_k\}\) be arbitrary sequences of natural numbers, and let a function \(f\in L(\ln^+L)^2(\mathbb T^2)\), then the sequence of its Fourier sum \(S_{m_k,n_k}(f,x,y)=o(\ln k)\), for almost all points \((x,y)\in \mathbb T^2\).
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multiple trigonometric Fourier series
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almost everywhere convergence
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