Approximate solution of periodic Riemann boundary value problem for analytic functions

A direct method for the approximate solution of periodic Riemann boundary value problems for analytic functions is given through the approximation by complex splines. By the δ-cardinal splines of the first degree we get the approximation of the canonical function based on the approximate result of singular integrals with Hilbert kernel. Furthermore, we obtain the approximate solution which may be sufficiently close to the exact solution to any degree when the partition Δ is sufficiently fine.