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Vladikavkazskii Matematicheskii Zhurnal, 2016, Volume 18, Number 3, Pages 43–59 (Mi vmj589)  
On mean convergence of Fourier–Jacobi series

E. J. Ibrahimov

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan
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Abstract: 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.
Key words: basis, optimal sequence, Fourier–Jacobi series, Vallee-Poussin sums, generalized shift function.
Received: 11.12.2015
Document Type: Article
UDC: 517.518
Language: Russian
Citation: E. J. Ibrahimov, “On mean convergence of Fourier–Jacobi series”, Vladikavkaz. Mat. Zh., 18:3 (2016), 43–59
Citation in format AMSBIB
\Bibitem{Ibr16}
\by E.~J.~Ibrahimov
\paper On mean convergence of Fourier--Jacobi series
\jour Vladikavkaz. Mat. Zh.
\yr 2016
\vol 18
\issue 3
\pages 43--59
\mathnet{http://mi.mathnet.ru/vmj589}
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