Operator representations of sequences and dynamical sampling

Ole Christensen, Marzieh Hasannasab, Diana T. Stoeva

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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 languageEnglish
JournalSampling Theory in Signal and Image Processing
Number of pages14
ISSN1530-6429
Publication statusAccepted/In press - 2020

Keywords

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

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