Periodic Spline Interpolation on Uniform Meshes

Abstract

Abstract We examine the interpolation with periodic polynomial splines of degree d and defect r ( d ≦ r ) on equidistant partitions of the real axis and generalize known results for r = 0. We prove necessary and sufficient conditions for the existence and a certain L 2 ‐stability of the interpolants as well as their approximation properties in the scale of the periodic SOBOLEV spaces.