On periodic L2 n-widths.

In this paper we study the n-width problem for the Sobolev space of periodic functions, Hperr(0,2π). Building on a theorem of Pinkus we show that it admits optimal even-dimensional spline spaces of all degrees ≥r−1. Then, by using a theorem of Karlovitz, we show that it does not admit any optimal spline space of odd dimension >1.