On periodic L2 n-widths

Abstract

In this paper we study the n -width problem for the Sobolev space of periodic functions, H per r ( 0 , 2 π ) . 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 .