English

On 2-dimensional mobile sampling

Classical Analysis and ODEs 2022-08-22 v1 Complex Variables

Abstract

Necessary and sufficient conditions are presented for several families of planar curves to form a set of stable sampling for the Bernstein space BΩ\mathcal{B}_{\Omega} over a convex set ΩR2\Omega \subset \mathbb{R}^2. These conditions "essentially" describe the mobile sampling property of these families for the Paley-Wiener spaces PWΩp,1p<\mathcal{PW}^p_{\Omega},1\leq p<\infty.

Cite

@article{arxiv.2005.11193,
  title  = {On 2-dimensional mobile sampling},
  author = {Alexander Rashkovskii and Alexander Ulanovskii and Ilya Zlotnikov},
  journal= {arXiv preprint arXiv:2005.11193},
  year   = {2022}
}

Comments

24 pages, 1 figure

R2 v1 2026-06-23T15:44:28.855Z