Localization property and Frames II
Commun. Korean Math. Soc. 2006 Vol. 21, No. 1, 101-115
Printed March 1, 2006
Young-Hwa Ha, Ju-Yeon Ryu
Ajou University, Ajou University
Abstract : 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.
Keywords : frame, Bessel sequence, Riesz basis, exponentially localized, polynomially localized, localization of frames
MSC numbers : 42C15, 46E99, 46B15
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