Uniqueness theorem for Hilbert transform for Boehmians (Q2813455)
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scientific article; zbMATH DE number 6597841
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniqueness theorem for Hilbert transform for Boehmians |
scientific article; zbMATH DE number 6597841 |
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24 June 2016
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generalized functions
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Boehmians
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Fourier transform
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Hilbert transform
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uniqueness theorem
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Uniqueness theorem for Hilbert transform for Boehmians (English)
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The author proves that, if an equivalent class \(F=[\frac{f_n}{\delta_n}]\) is a Boehmian of analytic type, namely, the values of the Hilbert transform \(\widetilde{F}\) of \(F\) on all negative integers are all zero, then \(F\) satisfies the uniqueness property that, if \(F=0\) on some open arc \(\Omega\), then \(F\equiv0\).
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