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.
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Christensen, O., Hasannasab, M. & Stoeva, D.T. Operator Representations of Sequences and Dynamical Sampling. STSIP 17, 29–42 (2018). https://doi.org/10.1007/BF03549611
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DOI: https://doi.org/10.1007/BF03549611