On uniform approximation in \(\mathbb R^2\) of continuous Banach-valued functions (Q863678)
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scientific article; zbMATH DE number 5122306
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On uniform approximation in \(\mathbb R^2\) of continuous Banach-valued functions |
scientific article; zbMATH DE number 5122306 |
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On uniform approximation in \(\mathbb R^2\) of continuous Banach-valued functions (English)
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5 February 2007
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Given a Banach space \(X\), a family of linear operators \(V\) is constructed such that \(Vf\) is a uniform approximation to \(f\) for every continuous function \(f: {\mathbb R}^2 \to X\) having bounded variation in the sense of Hardy. Estimates of the error \(f-Vf\) in terms of the second order modulus of continuity \(\omega_2(f)\) are obtained. Some notations and the overall motivation of the article are unclear.
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uniform
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Banach-valued
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bounded variation
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modulus of continuity
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