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

Ivana Slamić

• 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.