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

• Autores: Ivana Slamić
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 68, Fasc. 3, 2017, págs. 323-337
• Idioma: inglés
• DOI: 10.1007/s13348-016-0175-1
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• Resumen

  • 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.