On uniqueness of general orthogonal series. (Q1419876)
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scientific article; zbMATH DE number 2033466
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On uniqueness of general orthogonal series. |
scientific article; zbMATH DE number 2033466 |
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On uniqueness of general orthogonal series. (English)
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27 January 2004
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It is known that if a trigonometric series converges a.e. to 0 and \[ \lim_{\lambda\to\infty} \lambda \, \mu\{x: S^*(x)>\lambda\}=0 \] then all coefficients are equal to zero, where \(S^*(x)\) is the majorant of the series. The same is true for Haar, Walsh, Rademacher and Franklin systems. In this paper it is proved that this result is not valid for general orthogonal series.
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general orthogonal series
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uniqueness
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