A sufficient condition for mean convergence of orthogonal series for Freud weights (Q2724926)
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scientific article; zbMATH DE number 1618430
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A sufficient condition for mean convergence of orthogonal series for Freud weights |
scientific article; zbMATH DE number 1618430 |
Statements
12 July 2001
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mean convergence
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orthogonal series
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Freud weights
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Mhasker-Rahmanov-Saff number
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A sufficient condition for mean convergence of orthogonal series for Freud weights (English)
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A sufficient condition for the inequality NEWLINE\[NEWLINE\|S_n(f) Wu_b\|_{L_p(\mathbb{R})}\leq C\|fWu_B\|_{L_p(\mathbb{R})},NEWLINE\]NEWLINE (\(u_b(x)= (1+|x|)^b\), \(b,B\in R\), \(1< p< \infty\)) to hold is given, where \(S_n(f)\) is the \(n\)th partial sum of the orthonormal polynomial series expansion of \(f\) corresponding to a Freud weight \(W(x)= e^{-Q(x)}\).
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