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Unitary operators preserving wavelets


Authors: Ziemowit Rzeszotnik and Xiaofei Zhang
Journal: Proc. Amer. Math. Soc. 132 (2004), 1463-1471
MSC (2000): Primary 42C15
DOI: https://doi.org/10.1090/S0002-9939-03-07255-1
Published electronically: November 26, 2003
MathSciNet review: 2053354
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Abstract: We characterize a special class of unitary operators that preserve orthonormal wavelets. In the process we also prove that symmetric wavelet sets cover the real line.


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

  • [B] Bownik, M., On characterizations of multiwavelets in $L^{2}(\mathbb{R}^{n})$, Proc. Amer. Math. Soc. 129 (2001), 3265-3274. MR 2002g:42046
  • [GS] Garrigós, G. and Speegle, D., Completeness in the set of wavelets, Proc. Amer. Math. Soc. 128 (2000), 1157-1166. MR 2000i:42021
  • [HKLS] Ha, Y., Kang, H., Lee, J., and Seo, J., Unimodular wavelets for $L^{2}$ and the Hardy space $H^{2}$, Michigan Math. J. 41 (1994), 345-361. MR 95g:42050
  • [HW] Hernández, E. and Weiss, G., A first course on wavelets, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1996. MR 97i:42015
  • [L] Larson, D. R., Von Neumann algebras and wavelets, Operator algebras and applications (Samos, 1996), 267-312, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 495, Kluwer Acad. Publ., Dordrecht, 1997. MR 98g:46091
  • [R] Rzeszotnik, Z., Calderón's condition and wavelets, Collect. Math. 52 (2001), 181-191. MR 2002j:42039
  • [S] Speegle, D. M., The $s$-elementary wavelets are path-connected, Proc. Amer. Math. Soc. 127 (1999), 223-233. MR 99b:42045
  • [W] Weiss, G., personal communication.
  • [WUTAM] The Wutam Consortium, Basic properties of wavelets, J. Fourier Anal. Appl. 4 (1998), 575-594. MR 99i:42056
  • [Z] Zhang, X., Wavelet sets and frame sets, Ph. D. Thesis, Texas A&M University, 2002.

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Additional Information

Ziemowit Rzeszotnik
Affiliation: Institute of Mathematics, University of Wroclaw, Wroclaw, Poland; Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Email: zioma@math.utexas.edu

Xiaofei Zhang
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843

DOI: https://doi.org/10.1090/S0002-9939-03-07255-1
Keywords: Orthonormal wavelets, wavelet sets
Received by editor(s): September 30, 2002
Received by editor(s) in revised form: January 12, 2003
Published electronically: November 26, 2003
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society

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