Rational approximation to harmonic functions (Q1805903)

This is a very nice paper! The author generalizes the concepts of Padé-type and partial Padé-type approximants to the situation of approximating the Fourier series of a harmonic function. The main feature of this type of approximation is the liberty in prescribing poles for the approximating functions. Apart from the usual points of attention (existence, convergence, etc.) there is a section connected with Gaussian quadrature using an interpolating triangle consisting of the zeros of the polynomials orthogonal with respect to the linear functional that generates the rational approximants. The paper concludes with a set of interesting examples.