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Oblique projections, biorthogonal Riesz bases
and multiwavelets in Hilbert spaces


Author: Wai-Shing Tang
Journal: Proc. Amer. Math. Soc. 128 (2000), 463-473
MSC (2000): Primary 46C99, 47B99, 46B15
DOI: https://doi.org/10.1090/S0002-9939-99-05075-3
Published electronically: September 27, 1999
MathSciNet review: 1626494
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Abstract: In this paper, we obtain equivalent conditions relating oblique projections to biorthogonal Riesz bases and angles between closed linear subspaces of a Hilbert space. We also prove an extension theorem in the biorthogonal setting, which leads to biorthogonal multiwavelets.


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

  • 1. A. Aldroubi, Oblique projections in atomic spaces, Proc. Amer. Math. Soc. 124 (1996), 2051-2060. MR 96i:42020
  • 2. A. Cohen, I. Daubechies and J. C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. XLV (1992), 485-560. MR 93e:42044
  • 3. X. Dai and D. R. Larson, Wandering vectors for unitary systems and orthogonal wavelets, Mem. Amer. Math. Soc. 134 (1998), no. 640. MR 98m:47067
  • 4. I. C. Gohberg and M. G. Krein, Introduction to The Theory of Linear Nonselfadjoint Operators, Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, 1969. MR 39:7447
  • 5. T. N. T. Goodman, S. L. Lee and W. S. Tang, Wavelets in wandering subspaces, Trans. Amer. Math. Soc. 338 (1993), 639-654. MR 93j:42017
  • 6. T. N. T. Goodman, S. L. Lee and W. S. Tang, Wavelet bases for a set of commuting unitary operators, Adv. Comput. Math. 1 (1993), 109-126. MR 94h:42057
  • 7. P. R. Halmos, Introduction to Hilbert Spaces and Spectral Multiplicity, Chelsea, New York, 1951. MR 13:563a
  • 8. R. Q. Jia and Z. W. Shen, Multiresolution and wavelets, Proc. Edinburgh Math. Soc. 37 (1994), 271-300. MR 95h:42035
  • 9. S. L. Lee, H. H. Tan and W. S. Tang, Wavelet bases for a unitary operator, Proc. Edinburgh Math. Soc. 38 (1995), 233-260. MR 96g:42019
  • 10. J. B. Robertson, On wandering subspaces for unitary operators, Proc. Amer. Math. Soc. 16 (1965), 233-236. MR 30:5165
  • 11. M. Unser and A. Aldroubi, A general sampling theory for non-ideal acquisition devices, IEEE Trans. on Signal Processing 42 (1994), 2915-2925.
  • 12. R. M. Young, An Introduction to Nonharmonic Fourier Series, Academic Press, New York, 1980. MR 81m:42027

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Additional Information

Wai-Shing Tang
Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, 119260, Republic of Singapore
Email: mattws@math.nus.edu.sg

DOI: https://doi.org/10.1090/S0002-9939-99-05075-3
Keywords: Riesz basis, biorthogonal system, oblique projection, multiwavelets
Received by editor(s): March 23, 1998
Published electronically: September 27, 1999
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society

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