Properties of functions in the Wiener class \(\mathrm{BV}_p [a, b]\) for \(0 < p < 1\) (Q492570)
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scientific article; zbMATH DE number 6474227
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Properties of functions in the Wiener class \(\mathrm{BV}_p [a, b]\) for \(0 < p < 1\) |
scientific article; zbMATH DE number 6474227 |
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Properties of functions in the Wiener class \(\mathrm{BV}_p [a, b]\) for \(0 < p < 1\) (English)
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20 August 2015
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Summary: We will investigate properties of functions in the Wiener class \(\mathrm{BV}_p[a,b]\) with \(0<p<1\). We prove that any function in \(\mathrm{BV}_p[a,b]\) \((0<p<1)\) can be expressed as the difference of two increasing functions in \(\mathrm{BV}_p[a,b]\). We also obtain the explicit form of functions in \(\mathrm{BV}_p[a,b]\) and show that their derivatives are equal to zero a.e. on \([a,b]\).
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bounded \(p\)-variation
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Frechet space
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Jordan type decomposition
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