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arXiv · 1904.03434

Local average sampling and reconstruction with fundamental splines of fractional order

P. Devaraj·P. Massopust·S. Yugesh
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Abstract

We analyse sampling and average sampling techniques for fractional spline subspaces of $L^{2}({\mathbb{R}}).$ Fractional B-splines $\beta_{\sigma}$ are extensions of Schoenberg's polynomial splines of integral order to real order $\sigma > -1$. We present the interpolation with fundamental splines of fractional order for $\sigma \geq 1$ and the average sampling with fundamental splines of fractional order for $\sigma \geq \frac{3}{2}.$ Further, we generalise Kramer's lemma in the context of local average sampling.

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P. Devaraj, P. Massopust, S. Yugesh. 2019-04-06. Local average sampling and reconstruction with fundamental splines of fractional order. https://arxiv.org/abs/1904.03434

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