engleski

l^p -linear independence of the system of integer translates

Various properties of the system B_ψ of integer translates of a square integrable function ψ∈L2(R) can be completely described in terms of the periodization function p_ψ(ξ)=∑k∈Z|ψˆ(ξ+k)|2 . In this paper, we consider the problem of l^p -linear independence, where p>2 . The results we present include the method of construction for one type of counterexamples to several naturally taken conjectures, a new sufficient condition for l^p -linear independence and a characterization theorem having an additional assumption on B_ψ . In the latter, we obtain the characterization in terms of the sets of multiplicity of Lebesgue measure zero.

Integer translates ; l^p -linear independence ; sets of uniqueness

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