Sampling basis in reproducing kernel Banach spaces
Functional Analysis
2018-07-09 v1
Abstract
We present necessary and sufficient conditions to hold true a Kramer type sampling theorem over semi-inner product reproducing kernel Banach spaces. Under some sampling-type hypotheses over a sequence of functions on these Banach spaces it results necessary that such sequence must be a -Riesz basis and a sampling basis for the space. These results are a generalization of some already known sampling theorems over reproducing kernel Hilbert spaces.
Cite
@article{arxiv.1807.02218,
title = {Sampling basis in reproducing kernel Banach spaces},
author = {Hernán D. Centeno and Juan M. Medina},
journal= {arXiv preprint arXiv:1807.02218},
year = {2018}
}