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Oversampling generates super-wavelets

Author(s): Dorin Ervin Dutkay; Palle Jorgensen
Journal: Proc. Amer. Math. Soc. 135 (2007), 2219-2227.
MSC (2000): Primary 42C40, 47A20, 65T60, 94A20
Posted: 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: 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
Posted: February 6, 2007
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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