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DOI: 10.23671/VNC.2016.3.5876

On Mean Convergence of Fourier-Jacobi Series

Ibrahimov E. J.
Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 3.
The conditions on coefficients for mean convergence of Fourier-Jacobi series are obtained. The asymptotic formulae for the best approximation in Lebesgue spaces are derived and an asymptotic equality for Valee--Poussin sums is obtained. Some properties of generalized shift function are also studied.
Keywords: basis, optimal sequence, Fourier-Jacobi series, Vallee-Poussin sums, generalized shift function
Language: Russian Download the full text  
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