Localization property and frames. II. (English) Zbl 1162.42313
Summary: Localization of sequences with respect to Riesz bases for Hilbert spaces are comparable with perturbation of Riesz bases or frames. Gröchenig 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.
For part I, cf. Honam Math. J. 27, No. 2, 233–241 (2005).
For part I, cf. Honam Math. J. 27, No. 2, 233–241 (2005).
MSC:
| 42C15 | General harmonic expansions, frames |
| 46E99 | Linear function spaces and their duals |
| 46B15 | Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces |
