English

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

Functional Analysis 2023-11-15 v1 Information Theory Classical Analysis and ODEs math.IT

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.

Keywords

Cite

@article{arxiv.2311.08352,
  title  = {Sampling theorems with derivatives in shift-invariant spaces generated by periodic exponential B-splines},
  author = {Karlheinz Gröchenig and Irina Shafkulovska},
  journal= {arXiv preprint arXiv:2311.08352},
  year   = {2023}
}

Comments

40 pages, 3 figures

R2 v1 2026-06-28T13:21:01.272Z