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An Lp Saturation Theorem for Splines
Published online by Cambridge University Press: 20 November 2018
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Let 1 be a subdivision of [0, 1], and let
denote the class of functions whose restriction to each sub-interval
is a polynomial of degree at most k. Gaier [1] has shown that for uniform subdivisions △n (that is, subdivisions for which
if and only if f is a polynomial of degree at most k. Here, and subsequently, denotes the usual norm in Lp[0, 1], 1 ≦ p ≦ ∞, and we should emphasize that functions differing only on a set of Lebesgue measure zero are identified.
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