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 τ such that the corresponding interpolatory matrix possesses minimal condition or such that the related interpolation operator has minimal norm. We show that τ=0 is optimal in both cases. This improves known results of Merz, Reimer-Siepmann and Richards.