Optimal subspaces for mean square approximation of classes of differentiable functions on a segment (Q2227897)

The goal in this article is to find subspaces of square-integrable functions that give optimal approximations to approximants of certain function classes. Those are functions from Sobolev spaces \(W^{(r)}\) which are defined piecewise and with boundary conditions. The subspaces are generated by exponential splines. The latter are formulated by way of generalising the usual B-splines (which is always possible, e.g., via their Fourier transforms or otherwise).