On Weighted Average Interpolation with Cardinal Splines

Given a sequence of data with polynomial growth and an odd number , Schoenberg proved that there exists a unique cardinal spline of degree with polynomial growth such that for all . In this work, we show that this result also holds if we consider weighted average data , whenever the average function satisfies some light conditions. In particular, the interpolation result is valid if we consider cell-average data with . The case of even degree is also studied.