Mean and Almost Everywhere Convergence of Fourier-Neumann Series

摘要

Let J_#mu# denote the Bessel function of order #mu#. The functions x~(-#alpha#/2-#beta#/2-1/2)J_(#alpha#+#beta#+2n+1(x~(1/2)), n = 0, 1, 2, ..., form an orthogonal system in L~2((0, infinity), x~(#alpha#dx)-norm. Also, we describe the space in which the span of the system is dense and we show some of its properties. Finally, we study the almost everywhere convergence of the Fourier series for functions in such spaces.