General Mathematics, Vol. 4, 1996

Adrian Branga -- A fundamental property of B--splines

Abstract: Let $\Delta_{n}:t_{0}\leq t_{1}\leq \ldots \leq t_{n}$ be a division on the real line, where $n\in \mbox{\N}^{\ast}$ and $t_{0}, t_{1}, \ldots ,t_{n}\in \mbox{\R}$. We denote by $B_{i,k}(x)$, $k=0,\ldots ,n-1$, $i=0,\ldots ,n-1-k$, $x\in \mbox{\R}$, the functions $B$--spline coresponding to division $\Delta_{n}$.\\ \hspace*{1cm} Our aim in this paper is to prove a new fundamental property of $B$--splines.

Classification (MSC91): 65D07


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