Sampling in de Branges Spaces and Naimark Dilation
Complex Variables
2016-02-05 v1
Abstract
We consider the problem of sampling in de Branges spaces and develop some necessary conditions and some sufficient conditions for sampling sequences, which generalize some well-known sampling results in the Paley-Wiener space. These conditions are obtained by identifying the main construction with Naimark dilation of frames--embedding the de Branges space into a larger de Branges space while embedding the kernel functions associated with a sampling sequence into a Riesz basis for the larger space.
Cite
@article{arxiv.1602.01821,
title = {Sampling in de Branges Spaces and Naimark Dilation},
author = {Sa'ud al-Sa'di and Eric S. Weber},
journal= {arXiv preprint arXiv:1602.01821},
year = {2016}
}