Discrete Fourier-Neumann series

Let J(mu) denote the Bessel function of order mu. The system j(n)(x) = {j(n)(x)(s)}(sgreater than or equal to1) = {2rootalpha+2n+1 J(alpha+2n+1)(p(s))/ap(s)\J(alpha+1)(ap(s))\}(sgreater than or equal to1) with n = 0, 1,..., alpha > - 1, and where p(s) denotes the sth positive zero of J(alpha) (ax), is orthonormal in l(2) (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. (C) 2004 Elsevier Inc. All rights reserved.