Uniform convergence of \(N\)-dimensional trigonometric Fourier series (Q2709760)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniform convergence of \(N\)-dimensional trigonometric Fourier series |
scientific article |
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19 December 2001
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generalized bounded variation
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uniform convergence
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multiple Fourier series
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0.93721306
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0.9321171
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0.9306416
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Uniform convergence of \(N\)-dimensional trigonometric Fourier series (English)
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The author extends the notion of the generalized bounded variation introduced by \textit{H. Kita} and \textit{K. Yoneda} [Acta Math. Hung. 56, No. 3/4, 229-238 (1990; Zbl 0746.26007)] from functions of one variable to functions of \(N\) variables, and proves sufficient conditions for the uniform convergence (in Pringsheim's sense) of the multiple Fourier series of functions which are periodic in each variable, continuous and of generalized bounded variation on the \(N\)-dimensional torus. It is also proved that these sufficient conditions are best possible in some sense.
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