Periodic spline interpolation with shifted nodes (Q1314514)

Interpolation problems with periodic splines of defect 2 on an equidistant lattice with 2 shifted nodes in each knot interval are considered. Periodic Hermite-spline interpolation are considered. Periodic Hermite-spline interpolation is obtained as a special case. A simple criterion for existence and uniqueness of solution of the considered problem can be given using Euler-Frobenius polynomials and exponential Euler splines. In this way an old problem is solved and well- known result on periodic Lagrange-spline interpolation is generalized. An extension to cardinal spline interpolation is also shown.