An Lp Saturation Theorem for Splines
- 1 October 1972
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 24 (5) , 957-966
- https://doi.org/10.4153/cjm-1972-096-1
Abstract
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.Keywords
This publication has 1 reference indexed in Scilit:
- On the saturation class for spline functionsProceedings of the American Mathematical Society, 1972