Reconstruction from Radon projections and orthogonal expansion on a ball

The relation between Radon transform and orthogonal expansions of a function on the unit ball in \RR^d is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to algorithms for image reconstruction from Radon data. The relation between orthogonal expansion and the singular value decomposition of the Radon transform is also exploited.Comment: 15 page

Difference Quotients and Elliptic Mixed Boundary Problems of Second Order

Kaßmann M, Madych WR. Difference Quotients and Elliptic Mixed Boundary Problems of Second Order. Indiana University Mathematics Journal. 2007;56(3):1047-1082

SETS OF UNIQUENESS FOR SOLUTIONS OF THE REDUCED WAVE EQUATION

concerning functions v harmonic in the plane: Suppose v vanishes on the lines x = 0, y = 0 and y = ax, where a is a positive number; then v is identically zero. It is not difficult to see that this original conjecture fails for certain values of a. Nevertheless it did lead us to consider the nature of level sets for harmonic function