Localization of sequences with respect to Riesz bases for Hilbert
spaces are comparable with perturbation of Riesz bases or frames.
Gr\"{o}chenig first introduced the notion of localization. In this
thesis, 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.
