Best Approximation by Periodic Smooth Functions Original Research Article

LetWnbe the set of 2π-periodic functions with absolutely continuous (n−1)th derivatives and nth derivatives with essential suprema bounded by one. Letn>1. Best uniform approximations to a periodic continuous function fromWnare characterized. The result depends upon an analysis of the relation between the zeros, knots, and signs of periodic splines with simple knots. An appendix by O. V. Davydov states an alternative characterisation and demonstrates that the two characterisations are equivalent.