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Oversampling and preservation of tightness in affine frames

Author: Raquel G. Catalán
Journal: Proc. Amer. Math. Soc. 130 (2002), 1031-1034
MSC (2000): Primary 42C40
Published electronically: October 12, 2001
MathSciNet review: 1873776
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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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Additional Information

Raquel G. Catalán
Affiliation: Departamento de Matemática e Informática, Universidad Pública de Navarra, 31006, Pamplona, Spain

Keywords: Wavelets, frames, tight frames
Received by editor(s): September 3, 1999
Received by editor(s) in revised form: September 29, 2000
Published electronically: October 12, 2001
Additional Notes: This work was partially supported by the Spanish DGES PB97-1013, and originated during a stay at the Politecnico di Torino with the European TMR network on “Applications of the wavelet element method to boundary value problems".
Communicated by: David R. Larson
Article copyright: © Copyright 2001 American Mathematical Society