The Cauchy integral along \(\Phi\)-rectifiable curves (Q5925787)
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scientific article; zbMATH DE number 1566947
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Cauchy integral along \(\Phi\)-rectifiable curves |
scientific article; zbMATH DE number 1566947 |
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The Cauchy integral along \(\Phi\)-rectifiable curves (English)
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29 March 2001
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The author considers the Cauchy integral \(C(\Gamma,f,z)=\int_\Gamma \frac{f(\zeta)d\zeta}{\zeta-z}\) along a non-rectifiable curve \(\Gamma\). Preliminary, for certain classes of non-rectifiable curves it is studied an existence problem and properties of the Stieltjes integral \(\int_\Gamma f(z) dg(z)\). Basing on these results he treats the existence of a Cauchy integral and its boundary values along non-rectifiable curves. Some applications are also discussed.
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non-rectifiable curves
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Cauchy integral
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wavelet trajectories
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fractal curves
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