A Leibniz differentiation formula for positive operators (Q1849148)
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scientific article; zbMATH DE number 1836746
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Leibniz differentiation formula for positive operators |
scientific article; zbMATH DE number 1836746 |
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A Leibniz differentiation formula for positive operators (English)
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28 November 2002
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It is shown that for \(n\to\infty\) the Leibnizian combination \(L_n'(fg)-fL_n'(g)-gL_n'(f)\) converges uniformly to zero on a compact interval \(W\) if the positive operators belong to a certain class (including Bernstein, Gauss-Weierstrass and many others), and if the moduli of continuity of \(f,g\) satisfy a certain condition. A counterexample shows that Lipschitz conditions are not appropriate to produce a second-order version of this formula.
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positive linear operator
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exponential-type operator
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Lipschitz classes
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