engleski

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

Let T be a dual integrable representation of a countable discrete LCA group G acting on a Hilbert space H. We consider the problem of characterizing l^2(G)-linear independence of the system B_ψ={; ; ; T_g(ψ):g∈G}; ; ; for a given function ψ∈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 B_ψ is the Gabor system.

Dual integrable representation ; T-cyclic subspace ; Bracket function ; l^2(G)-linear independence ; Vilenkin group ; Gabor system

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