Kolmogorov's abstract theorem: application to metric spaces and topological groups (Q498213)
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scientific article; zbMATH DE number 6485684
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Kolmogorov's abstract theorem: application to metric spaces and topological groups |
scientific article; zbMATH DE number 6485684 |
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Kolmogorov's abstract theorem: application to metric spaces and topological groups (English)
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28 September 2015
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A very abstract version of Kolmogorov's theorem on the existence of an integrable function with almost everywhere divergent Fourier series [\textit{A. Kolmogoroff}, Fundam. Math. 4, 324--328 (1923; JFM 49.0205.02)] is obtained. It is applied to constructing a Fourier-Lebesgue series in bounded biorthonormal systems of complex-valued functions defined on metric spaces and topological groups such that these series diverge on a set of positive measure.
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Kolmogorov's theorem
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orthonormal system
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metric space
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topological group
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