Operator representations of sequences and dynamical sampling
Abstract
This paper is a contribution to the theory of dynamical sampling. Our purpose is twofold. We first consider representations of sequences in a Hilbert space in terms of iterated actions of a bounded linear operator. This generalizes recent results about operator representations of frames, and is motivated by the fact that only very special frames have such a representation. As our second contribution we give a new proof of a construction of a special class of frames that are proved by Aldroubi et al. to be representable via a bounded operator. Our proof is based on a single result by Shapiro \& Shields and standard frame theory, and our hope is that it eventually can help to provide more general classes of frames with such a representation.
Cite
@article{arxiv.1804.00077,
title = {Operator representations of sequences and dynamical sampling},
author = {Ole Christensen and Marzieh Hasannasab and Diana T. Stoeva},
journal= {arXiv preprint arXiv:1804.00077},
year = {2020}
}
Comments
Accepted for publication in Sampl. Theory Signal Image Process