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Sequence Dominance in Shift-Invariant Spaces

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Abstract

We show that a Bessel sequence \(B_\psi \) of integer translates of a square integrable function \(\psi \in L^2(\mathbb {R})\) has the Besselian property if and only if its periodization function \(p_\psi \) is bounded from below. We also give characterizations of Besselian and Hilbertian properties of a general sequence \(B_\psi \) of integer translates in terms of the classical notion of sequence dominance.

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Acknowledgements

The first author’s work has been supported by the Croatian Science Foundation under the project IP-2016-06-1046.

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  1. Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000, Zagreb, Croatia

    Tomislav Berić & Hrvoje Šikić

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  1. Tomislav Berić
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  2. Hrvoje Šikić
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Correspondence to Tomislav Berić.

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Communicated by Chris Heil.

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Berić, T., Šikić, H. Sequence Dominance in Shift-Invariant Spaces. J Fourier Anal Appl 26, 55 (2020). https://doi.org/10.1007/s00041-020-09765-3

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  • DOI: https://doi.org/10.1007/s00041-020-09765-3

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