On Fourier series with non-negative coefficients and two problems of R. P. Boas (Q1071986)
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scientific article; zbMATH DE number 3939932
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Fourier series with non-negative coefficients and two problems of R. P. Boas |
scientific article; zbMATH DE number 3939932 |
Statements
On Fourier series with non-negative coefficients and two problems of R. P. Boas (English)
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1985
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Let \(a_ k\geq 0\), \(b_ k\geq 0\) and \(g(x):=\sum^{\infty}_{k=1}b_ k\) sin(kx), \(f(x):=\sum^{\infty}_{k=1}a_ k\) cos(kx). Necessary and sufficient conditions on g resp. f are given such that \(\sum k^{2j+1}b_ k\) resp. \(\sum k^{2j}a_ k\) do converge.
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Fourier series
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nonnegative coefficients
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