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arXiv · 2311.08352

Sampling theorems with derivatives in shift-invariant spaces generated by periodic exponential B-splines

Karlheinz Gröchenig·Irina Shafkulovska
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Abstract

We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive samples. These conditions are near optimal, and, in particular, they imply the existence of sampling sets with lower Beurling density arbitrarily close to the necessary density.

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Karlheinz Gröchenig, Irina Shafkulovska. 2023-11-14. Sampling theorems with derivatives in shift-invariant spaces generated by periodic exponential B-splines. https://arxiv.org/abs/2311.08352

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