Generalization of an integral formula of Guessab and Schmeisser (Q610026)
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scientific article; zbMATH DE number 5822498
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalization of an integral formula of Guessab and Schmeisser |
scientific article; zbMATH DE number 5822498 |
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Generalization of an integral formula of Guessab and Schmeisser (English)
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1 December 2010
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The authors consider two-point quadrature formulas with symmetrically distributed nodes for weighted integrals. Using a generalized form of the classical Peano kernel theory, they prove best possible error estimates for such formulas in spaces of differentiable functions with a weighted \(L_p\)-norm (\(1 \leq p \leq \infty\)) whose weight depends on the weight of the original quadrature formula. Some special cases are considered in detail.
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weight function
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w-harmonic sequences of functions
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quadrature formula
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Gauss formula
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Legendre-Gauss
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Chebyshev-Gauss
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Hermite-Gauss
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inequality
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sharp constants
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best possible constants
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two-point quadrature formula
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0.8991435
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0.8990469
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0.8959579
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