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

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

Published electronically:
October 12, 2001

MathSciNet review:
1873776

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Abstract | References | Similar Articles | Additional Information

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

Keywords:
Wavelets,
frames,
tight frames

Received by editor(s):
September 3, 1999

Received by editor(s) in revised form:
September 29, 2000

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