S. Yugesh

Local average sampling and reconstruction with fundamental splines of fractional order

We analyse sampling and average sampling techniques for fractional spline subspaces of $L^{2}({\mathbb{R}}).$ 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 $σ\geq 1$ and the average sampling with fundamental splines of fractional order for $σ\geq \frac{3}{2}.$ Further, we generalise Kramer's lemma in the context of local average sampling.