Optimal shift parameters for periodic spline interpolation

Using the exponential Euler spline, restricted on the unit circle, we sketch a unified approach to the periodic spline interpolation with shifted interpolation nodes. Mainly we are interested in the optimal choice of the shift parameter such that the corresponding interpolatory matrix possesses minimal condition or such that the related interpolation operator has minimal norm. We show that =0 is optimal in both cases. This improves known results of Merz, Reimer-Siepmann and Richards.