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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Oversampling generates super-wavelets


Authors: Dorin Ervin Dutkay and Palle Jorgensen
Journal: Proc. Amer. Math. Soc. 135 (2007), 2219-2227
MSC (2000): Primary 42C40, 47A20, 65T60, 94A20
Published electronically: February 6, 2007
MathSciNet review: 2299499
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Abstract: We show that the second oversampling theorem for affine systems generates super-wavelets. These are frames generated by an affine structure on the space $ \underbrace{L^2(\mathbb{R}^d) \oplus...\oplus L^2(\mathbb{R}^d)}_{p \mbox{times}}$.


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Additional Information

Dorin Ervin Dutkay
Affiliation: Department of Mathematics, University of Central Florida, P.O. Box 161364, Orlando, Florida 32816-1364
Email: ddutkay@mail.ucf.edu

Palle Jorgensen
Affiliation: Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242
Email: jorgen@math.uiowa.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08724-2
PII: S 0002-9939(07)08724-2
Keywords: Wavelet, frame, sampling, oversampling, affine, scaling, lattice, interpolation, dilations, extensions, super wavelets, operators, frames, Hilbert space
Received by editor(s): November 16, 2005
Received by editor(s) in revised form: March 28, 2006
Published electronically: February 6, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.