Strong Unicity of Best Uniform Approximations from Periodic Spline Spaces

Abstract

In this paper we give a complete characterization of the strongly unique best uniform approximations from periodic spline spaces. We distinguish between even-dimensional and odd-dimensional periodic spline spaces. These spaces are weak Chebyshev if and only if their dimension is odd. We show that the strongly unique best approximation from periodic spline spaces of odd dimension can be characterized alone by alternation properties of the error. This is not the case for even dimension. In this case an additional interpolation condition arises in our characterization.