Regularity for Complete and Minimal Gabor Systems

Abstract

Nonsymmetrically weighted extensions of the Balian– Low theorem are proved for Gabor systems G(g,1,1) that are complete and minimal in L(R). For g ∈ L(R), it is proved that if 3< p≤ 4≤ q <∞ satisfy 3/p+ 1/q = 1 and ∫ |x||g(x)| dx <∞ and ∫ |ξ||ĝ(ξ)| dξ < ∞ then G(g,1,1) = {eg(x − k)}k,n∈Z cannot be complete and minimal in L(R). For the endpoint case (p, q… (More)

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