A discretized Fourier orthogonal expansion in orthogonal polynomials on a cylinder

We study the convergence of a discretized Fourier orthogonal expansion in orthogonal polynomials on B2×[−1,1]B2×[−1,1], where B2B2 is the closed unit disk in R2R2. The discretized expansion uses a finite set of Radon projections and provides an algorithm for reconstructing three-dimensional images in computed tomography. The Lebesgue constant is shown to be of asymptotic order m(log(m+1))2, and convergence is established for functions in C2(B2×[−1,1])C2(B2×[−1,1]).