Peano kernels and the Euler-Maclaurin formula (Q2721578)
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scientific article; zbMATH DE number 1616251
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Peano kernels and the Euler-Maclaurin formula |
scientific article; zbMATH DE number 1616251 |
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27 May 2002
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linear functionals
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Peano kernels
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Euler-Maclaurin formula
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0.86708057
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0.8614899
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Peano kernels and the Euler-Maclaurin formula (English)
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This paper is concerned with certain linear functionals \(L(f)\) on spaces of differentiable functions. When a functional satisfies \(L(p_m)=0\) for all polynomials \(p_m\) of degree at most \(m\) it can be represented as an integral transform with the Peano kernel \(K_m\) of \(L\) of order \(m\). It is shown that certain symmetry properties of \(L\) correspond to symmetry properties of the kernel \(K_m\). These results are used to characterize those functionals \(L\) for which an Euler-Maclaurin expansion exists. Among these are the error terms of numerical integration and differentiation formulas.
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