On mean convergence of Fourier–Jacobi series

E. J. Ibrahimov

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan

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.

UDC: 517.518

Received: 11.12.2015