A Discretized Fourier Orthogonal Expansion in Orthogonal Polynomials on a Cylinder

Abstract

We study the convergence of a discretized Fourier orthogonal expansion in orthogonal polynomials on $B^2 \times [-1,1]$, where $B^2$ is the closed unit disk in $\RR^2$. 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 $m \, (\log(m+1))^2$, and convergence is established for functions in $C^2(B^2 \times [-1,1])$.