On the Kolmogorov complexity of functions of finite smoothness (Q1080660)
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scientific article; zbMATH DE number 3967916
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Kolmogorov complexity of functions of finite smoothness |
scientific article; zbMATH DE number 3967916 |
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On the Kolmogorov complexity of functions of finite smoothness (English)
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1986
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The \(\epsilon\)-complexity, in the sense of Kolmogorov, of the class \(W^ r_ 1=\{f: [0,1]\to [-1,1],\) \(f^{(r-1)}\) is absolutely continuous, \(\int^{1}_{0}| f^{(r)}(x)| dx\leq 1\}\), \(r>1\), is asymptotically equal to \((1/\epsilon)^{1/r}/\log (1/\epsilon)\).
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