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The convergence of discrete Fourier-Jacobi series. (English) Zbl 1437.42002

Summary: The discrete counterpart of the problem related to the convergence of the Fourier-Jacobi series is studied. To this end, given a sequence, we consider the analogue of the partial sum operator related to Jacobi polynomials and characterize its convergence in the \(\ell^p(\mathbb{N})\)-norm.

MSC:

42A20 Convergence and absolute convergence of Fourier and trigonometric series
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

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References:

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