engleski

l^p(G)-Linear Independence and p-Zero Divisors

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^p(G) -linear independence ( p≠2 ) of the system {; ; ; T_kψ:k∈G}; ; ; for the given ψ∈H , which we previously studied in the context of the integer translates of a square integrable function. The extensions of the known results for translates to this setting are obtained using a slightly different approach, through which we show that, under certain conditions, this problem is related to the ‘Wiener’s closure of translates’ problem and the problem of the existence of p-zero divisors, arising around the zero divisor conjecture in algebra. Using this connection, we also obtain several improvements for the case of the integer translates.

bracket function ; cyclic vector ; dual integrable representation ; l^p(G) -linear independence ; zero divisor

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