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Oversampling and preservation of tightness in affine frames

Author(s): Raquel G. Catalán
Journal: Proc. Amer. Math. Soc. 130 (2002), 1031-1034.
MSC (2000): Primary 42C40
Posted: 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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Additional Information:

Raquel G. Catalán
Affiliation: Departamento de Matemática e Informática, Universidad Pública de Navarra, 31006, Pamplona, Spain
Email: raquel.garcia@unavarra.es

DOI: 10.1090/S0002-9939-01-06187-1
PII: S 0002-9939(01)06187-1
Keywords: Wavelets, frames, tight frames
Received by editor(s): September 3, 1999
Received by editor(s) in revised form: September 29, 2000
Posted: 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
Copyright of article: Copyright 2001, American Mathematical Society

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