Strong and weak weighted convergence of Jacobi series (Q1352908)
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scientific article; zbMATH DE number 980678
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Strong and weak weighted convergence of Jacobi series |
scientific article; zbMATH DE number 980678 |
Statements
Strong and weak weighted convergence of Jacobi series (English)
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8 April 1997
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Let \(\{p_n^{(\alpha,\beta)}(x)\}\) \((n=0,1,2,\dots\); \(\alpha,\beta>-1)\) be the sequence of the orthogonal Jacobi polynomials and \((S_Nf)(x)= \sum^N_{k=0}a_k p_k^{(\alpha,\beta)}(x)\) the \(N\)-th partial sum of the Fourier-Jacobi series of the function \(f\). The necessary and sufficient conditions for the strong and weak weighted convergence of Fourier-Jacobi series are obtained.
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weighted norm inequalities
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Fourier-Jacobi series
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strong and weak weighted convergence
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