This paper discusses generalized interpolating splines which determined by n order linear differential operators, and the best operators of interpolating approximation in W2m spaces, The explicit constructive method for the reproducing kernel in W2m space is presented, and proves the uniformity of spline interpolating operators and the best operators of interpolating approximation W2m space by reproducing kernel. The explicit expression of approximation error on a bounded ball in W2m space, and error estimation of spline operator of approximation are obtained.
