LAUSR

Given a sequence of data {yn}n∈Z$\{ y_{n} \} _{n \in \mathbb{Z}}$ with polynomial growth and an odd number d$d$, Schoenberg proved that there exists a unique cardinal spline f$f$ of degree d$d$ with polynomial growth such that f(n)=yn$f ( n ) =y_{n}$ for all n∈Z$n\in \mathbb{Z}$. In this work, we show that this result also holds if we consider weighted average data f∗h(n)=yn$f\ast h ( n ) =y_{n}$, whenever the average function h$h$ satisfies some light conditions. In particular, the interpolation result is valid if we consider cell-average data ∫n−an+af(x)dx=yn$\int_{n-a}^{n+a}f ( x ) dx=y_{n}$ with 0