Semi-cardinal polyspline interpolation with Beppo Levi boundary conditions

We consider the problem of interpolation to a sequence of n-variate periodic data functions prescribed on {j}×Rn, j∈Z+, from a space of piecewise polyharmonic functions (polysplines) of n+1 variables. A unique solution is obtained subject to boundary conditions of the type employed in Duchon's theory of polyharmonic surface splines. The construction of the polyspline scheme is based on the extension of Schoenberg's semi-cardinal interpolation model to a class of univariate L-splines.