ABSTRACT
Analogously to the case of algebraic polynomials we are able to go over to periodic spline functions. For simplicity, we restrict ourselves to splines with respect to Δ-derivatives in this preparatory part. As reference space for spline approximation we use a Sobolev-like space, in which spline interpolation may be understood as minimum norm procedure under consistency to the given data points. Best approximate integration is seen in the context of integrating periodic spline interpolants.
