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Wavelet subspaces invariant under groups of translation operators

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Abstract

We study the action of translation operators on wavelet subspaces. This action gives rise to an equivalence relation on the set of all wavelets. We show by explicit construction that each of the associated equivalence classes is non-empty.

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References

  1. Behera B and Madan S, Characterization of a class of band-limited wavelets, to appear inJ. Comput. Anal. Appl.

  2. Dai X and Larson D, Wandering vectors for unitary systems and orthogonal wavelets,Memoirs Am. Math. Soc. 640 (1998)

  3. Gripenberg G, A necessary and sufficient condition for the existence of a father wavelet,Studia Math. 114 (1995) 207–226

    MATH  MathSciNet  Google Scholar 

  4. Ha Y-H, Kang H, Lee J and Seo J, Unimodular wavelets forL 2 and the Hardy spaceH 2,Michigan Math. J. 41 (1994) 345–361

    Article  MATH  MathSciNet  Google Scholar 

  5. Hernández E and Weiss G,A first course on wavelets (1996) (Boca Raton: CRC Press)

    MATH  Google Scholar 

  6. Madych W R, Some elementary properties of multiresolution analyses of L2(ℝn), in: Wavelets — A tutorial in theory and applications (ed.) C K Chui (1992) (Boston: Academic Press) pp. 259–294

    Google Scholar 

  7. Mallat S, Multiresolution approximations and wavelet orthonormal bases of L2(ℝ),Trans. Am. Math. Soc. 315 (1989) 69–87

    Article  MATH  MathSciNet  Google Scholar 

  8. Meyer Y, Ondelettes, fonctions splines et analyses graduées,Rend. Sem. Mat. Univ. Politec. Torino 45 (1988) 1–42

    Google Scholar 

  9. Schaffer S and Weber E, Wavelets having the translation invariance property of ordern, preprint (2000)

  10. Walter G, Translation and dilation invariance in orthogonal wavelets,Appl. Comput. Harmon. Anal. 1 (1994) 344–349

    Article  MATH  MathSciNet  Google Scholar 

  11. Walter G, Wavelets and other orthogonal systems with applications (1994) (Boca Raton: CRC Press)

    MATH  Google Scholar 

  12. Wang X, The study of wavelets from the properties of their Fourier transforms, Ph.D. thesis (1995) (Washington University in St. Louis)

  13. Weber E, On the translation invariance of wavelet subspaces,J. Fourier Anal. Appl. 6 (2000) 551–558

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, 208 016, Kanpur, India

    Biswaranjan Behera & Shobha Madan

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  1. Biswaranjan Behera
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  2. Shobha Madan
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Correspondence to Biswaranjan Behera.

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Behera, B., Madan, S. Wavelet subspaces invariant under groups of translation operators. Proc. Indian Acad. Sci. (Math. Sci.) 113, 171–178 (2003). https://doi.org/10.1007/BF02829766

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  • DOI: https://doi.org/10.1007/BF02829766

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