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.
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