When an orthogonal series is a Fourier series? (Q1889515)
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scientific article; zbMATH DE number 2121021
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | When an orthogonal series is a Fourier series? |
scientific article; zbMATH DE number 2121021 |
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When an orthogonal series is a Fourier series? (English)
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2 December 2004
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\textit{W. Orlicz} [Studia 1, 1--39, 241--255 (1929; JFM 55.0164.02)] proved conditions necessary and sufficient for a series with respect to an orthonormal system to be the Fourier series of a function from a certain class. These conditions are expressed in terms of regular mean values of the orthogonal series in question. The present author observes that Orlicz' proof works in a more general situation, and it is the theme of this note.
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Fourier series
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orthonormal system
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Orlicz space
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0.7894496
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0.7888572
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0.77144456
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0.77080286
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0.7704718
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