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On MRA Riesz wavelets


Author: R. A. Zalik
Journal: Proc. Amer. Math. Soc. 135 (2007), 787-793
MSC (2000): Primary 42C40
DOI: https://doi.org/10.1090/S0002-9939-06-08531-5
Published electronically: September 11, 2006
MathSciNet review: 2262874
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Abstract: We investigate the properties of univariate MRA Riesz wavelets. In particular we obtain a generalization to semiorthogonal MRA wavelets of a well-known representation theorem for orthonormal MRA wavelets.


References [Enhancements On Off] (What's this?)

  • 1. J. J. Benedetto and D. F. Walnut, Gabor frames for $ L^2$ and related spaces, in ``Wavelets: Mathematics and Applications'' (J. J. Benedetto and M. W. Frazier, Eds.), pp. 97-162, CRC Press, Boca Raton, FL, 1994. MR 1247515 (94i:42040)
  • 2. O. Christensen, ``An Introduction to Frames and Riesz Bases", Birkhäuser, Boston, 2003. MR 1946982 (2003k:42001)
  • 3. C. K. Chui, ``An Introduction to Wavelets," Academic Press, San Diego, 1992. MR 1150048 (93f:42055)
  • 4. C. K. Chui and X. Shi, Inequalities of Littlewood-Paley type for frames and wavelets, SIAM J. Math. Anal. 24 (1993), 263-277. MR 1199539 (94d:42039)
  • 5. S. J. Favier and R. A. Zalik, On the stability of frames and Riesz bases, Appl. Comput. Harm. Anal. 2 (1995), 160-173. MR 1325538 (96e:42030)
  • 6. E. Hernández and G. Weiss, ``A First Course on Wavelets", CRC Press, Boca Raton, FL, 1996. MR 1408902 (97i:42015)
  • 7. R. M. Young, ``An Introduction to Nonharmonic Fourier Series'', Revised $ 1^{\text{st}}$ ed., Academic Press, San Diego, 2002. MR 1836633 (2002b:42001)

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Additional Information

R. A. Zalik
Affiliation: Department of Mathematics and Statistics, Auburn University, Auburn, Alabama 36849–5310
Email: zalik@auburn.edu

DOI: https://doi.org/10.1090/S0002-9939-06-08531-5
Keywords: Bessel wavelets, frame wavelets, Riesz wavelets, semiorthogonal wavelets, multiresolution analysis.
Received by editor(s): January 30, 2004
Received by editor(s) in revised form: October 13, 2005
Published electronically: September 11, 2006
Additional Notes: The author is grateful to Alfredo L. González and David R. Larson for their helpful comments.
Communicated by: David R. Larson
Article copyright: © Copyright 2006 American Mathematical Society

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