Sharp results on sampling with derivatives in shift-invariant spaces and multi-window Gabor frames
Classical Analysis and ODEs
2022-05-04 v2
Abstract
We study the problem of sampling with derivatives in shift-invariant spaces generated by totally-positive functions of Gaussian type or by the hyperbolic secant. We provide sharp conditions in terms of weighted Beurling densities. As a by-product we derive new results about multi-window Gabor frames with respect to vectors of Hermite functions or totally positive functions.
Cite
@article{arxiv.1712.07899,
title = {Sharp results on sampling with derivatives in shift-invariant spaces and multi-window Gabor frames},
author = {Karlheinz Gröchenig and José Luis Romero and Joachim Stöckler},
journal= {arXiv preprint arXiv:1712.07899},
year = {2022}
}
Comments
22 pages