Local Average Sampling and Reconstruction with Fundamental Splines of Fractional Order. (27th July 2019) - Devaraj, P.; Massopust, Peter; Yugesh, S.
Abstract: We analyze sampling and average sampling techniques for fractional spline subspaces of L 2 ( R ) . Fractional B-splines β σ are extensions of Schoenberg's polynomial splines of integral order to real order σ > − 1 . We present the interpolation with fundamental splines of fractional order for σ ≥ 1 and the average sampling with fundamental splines of fractional order for σ ≥ 3 2 . Further, we generalize Kramer's lemma in the context of local average sampling.