Oversampling and preservation of tightness in affine frames

Catalán, Raquel

doi:10.1090/S0002-9939-01-06187-1

Oversampling and preservation of tightness in affine frames
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by Raquel G. Catalán

Proc. Amer. Math. Soc. 130 (2002), 1031-1034

DOI: https://doi.org/10.1090/S0002-9939-01-06187-1

Published electronically: October 12, 2001

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Abstract:

The problem of how an oversampling of translations affects the bounds of an affine frame has been proposed by Chui and Shi. In particular, they proved that tightness is preserved if the oversampling factor is coprime with the dilation factor. In this paper we study, in the dyadic dilation case, oversampling of translation by factors which do not satisfy the above condition, and prove that tightness is preserved only in the case of affine frames generated by wavelets having frequency support with very particular properties.

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