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Perturbation of frame sequences and its applications to shift-invariant spaces. (English) Zbl 1106.42025
Summary: We generalize the main result in [O. Christensen, H. O. Kim, R.Y. Kim, and J. K. Lim [J. Geom. Anal. 15, 181–191 (2005; Zbl 1087.42022)] in order to make it comparable with existing results. Then we compare the special cases of the three results in the literature in the setting of the perturbation of the generating sets of finitely generated shift-invariant spaces of L 2 ( d ).
42C30Completeness of sets of functions of non-trigonometric Fourier analysis
46A35Summability and bases in topological linear spaces
42C15General harmonic expansions, frames