Discrete Fourier–Neumann series

AbstractLet Jμ denote the Bessel function of order μ. The systemjnα={jnα(s)}s⩾1=2α+2n+1Jα+2n+1(ps)aps|Jα+1(aps)|s⩾1with n=0,1,…,α>−1, and where ps denotes the sth positive zero of Jα(ax), is orthonormal in l2(N). In this paper, we study the mean convergence of the Fourier series with respect to this system. Also, we describe the space in which the span of the system is dense