We prove that if (PHI_j~ (2 pi n)) and (phi_j~ (2 pi n)) are in l~2 (Z), then (PHI_j(x - 1/2~j), phi_j(x - 1/2~j)) (l chemical bounds 0, - , 2~j - 1) is biorthogonal if and only if for each l chemical bounds 0, - , 2~j - 1, there is a positive constant C such that sum from alpha delong to (is member of ) the set Z |PHI_j~(2 pi (l + 2~j alpha)) phi_j~(-) (2 pi (l + 2~j alpha)) | >= C, where PHI_j chemical bounds 2~(-j/2) PHI_j~ and phi_j chemical bounds 2~(-j/2) phi_j~.
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