Periodic interpolation with a minimum norm of the $m$-th derivative

In this paper, the interpolation problem for periodic data with a bounded lp-norm is investigated for an interpolating set of smooth periodic functions. In the cases when $p=2$ and $p=\infty$, the exact values of the $L_p$-norms of the $m$-th derivative of the best interpolants are found for a certain class of sequences.