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Localization of sequences with respect to Riesz bases for Hilbert
spaces are comparable with perturbation of Riesz bases or frames.
Gr$\rm\ddot{o}$chenig first introduced the notion of localization.
We introduce more general definition of localization and show that
exponentially localized sequences and polynomially localized
sequences with respect to Riesz bases are Bessel sequences.
Furthermore, they are frames provided some additional conditions
are satisfied.
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