### 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.

Original language | English |
---|---|

Journal | Sampling Theory in Signal and Image Processing |

Number of pages | 14 |

ISSN | 1530-6429 |

Publication status | Accepted/In press - 2020 |

### Keywords

- Frames, operator representation
- Dynamical sampling
- Schauder basis
- the Carleson condition
- Hardy space

## Cite this

Christensen, O., Hasannasab, M., & Stoeva, D. T. (Accepted/In press). Operator representations of sequences and dynamical sampling.

*Sampling Theory in Signal and Image Processing*.