COMPLEX SPLINE FUNCTIONS

Complex spline functions play an important role in approximation theory of analytic functions,and the interpolation problem has a fundamental significance in that theory. As is known, Ahlberg,Nilson, and Walsh have obtained good results about the interpolation problem of splines with equi-distant node points. If the node points are arbitrarily scattered, then the interpolation problem is stillopen. In this paper, we have changed the interpolation problem of complex splines to the equivalentproblem of real splines, and solved the problem for n = 2 and n = 3.