Regularization of a continuation problem for electrodynamic equations

The problem of continuation of a solution of electrodynamic equations from the time-like half-plane S = { x ∈ R 3 |x 3 = 0 } inside the half-space R + 3 = { x ∈ R 3 x 3 > 0 } is considered. A regularization method for a solution of this problem with approximate data is proposed, and the convergence of this method for the class of functions that are analytic with respect to space variables is stated.