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\(\ell ^2(G)\)-linear independence for systems generated by dual integrable representations of LCA groups

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Abstract

Let T be a dual integrable representation of a countable discrete LCA group G acting on a Hilbert space \(\mathbb H\). We consider the problem of characterizing \(\ell ^2(G)\)-linear independence of the system \(\mathcal B_{\psi }=\{T_{g}\psi :g\in G\}\) for a given function \(\psi \in \mathbb H\) in terms of the bracket function. The characterization theorem is obtained for the case when G is a uniform lattice of the p-adic Vilenkin group acting by translations and a partial answer is given for the case when \(\mathcal B_{\psi }\) is the Gabor system.

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  1. Department of Mathematics, University of Rijeka, R. Matejčić 2, 51000, Rijeka, Croatia

    Ivana Slamić

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  1. Ivana Slamić
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Correspondence to Ivana Slamić.

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The research of the author has been supported in part by University of Rijeka research Grant 13.14.1.2.02.

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Slamić, I. \(\ell ^2(G)\)-linear independence for systems generated by dual integrable representations of LCA groups. Collect. Math. 68, 323–337 (2017). https://doi.org/10.1007/s13348-016-0175-1

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