Accurate computation of multi-dimensional Riesz potentials

The paper discusses a fast method for computing the Riesz potentials in the framework of the method approximate approximations. By combining high-order cubature formulas with tensor product approximations, we derive an approximation of the potentials which is fast, accurate and provides approximation formulas of high order. The action of volume poten- tials on the basis functions introduced in the theory of approximate approximations allows one-dimensional integral representations with separable integrands, i.e. a product of functions depending on only one of the variables. Then a separated representation of the density, com- bined with a suitable quadrature rule, leads to a tensor product representation of the integral operator. Since only one-dimensional operations are used, the resulting method is effective also in the high-dimensional case.