Optimal spline spaces for $L^2$ $n$-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 $\ge r-1$, and all these spline spaces have uniform knots.

17 pages, 4 figures. Fixed a typo. Article published in Constructive Approximation

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