Error estimates in projective solutions of the Radon equation

Abstract

The model Radon equation is the integral equation of the second kind defined by the interior limit of the electrostatic double-layer potential relative to a curve with one angular point and characterized by the noncompactness of the operator with respect to the maximum norm. It is shown that the solution to this equation is decomposable into a regular part and a finite linear combination of intrinsic singular functions. The maximal regularity of the solution and explicit formulae for the coefficients of the singular functions are given. The regularity permits to specify how slow the convergence of the classical projection method is, while the abovementioned formulae lead to modified projection methods of the dual singular function method type, with better approximations for the solution and for the coefficients of singularities.