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We construct a uniformly discrete sequence { λ 1 < λ 2 < ⋯ } ⊂ R and functions g and { g n ⁎ } in L 2 ( R ) , such that every f ∈ L 2 ( R ) admits a series expansion f ( x ) = ∑ n = 1 ∞ 〈 f , g n ⁎ 〉 g ( x − λ n ) convergent in the L 2 ( R ) norm.