Admissible boundary conditions at an irregular singular point for systems of linear ordinary differential equations

A class of admissible boundary conditions at an irregular singular point is distinguished, and the behavior in its neighborhood of the linear relations between the values of the system solutions, which are generated by these conditions, is described. In particular, it is shown under what assumptions the radiation conditions are admissible boundary conditions at infinity for a system of second-order equations, and when and how the conditions can be transferred to a finite point when solving a singular boundary value problem numerically.