Optimal Spline Spaces for $$L^2$$ L 2 n-Width Problems with Boundary Conditions

Abstract

In this paper we show that, with respect to the $L^2$ norm, three classes of functions in $H^r(0,1)$, defined by certain boundary conditions, admit optimal spline spaces of all degrees $\geq r-1$, and all these spline spaces have uniform knots.