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Haar Type Orthonormal Wavelet Bases in R2

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Abstract

K.-H. Grochenig and A. Haas asked whether for every expanding integer matrix A ∈ Mn(ℤ) there is a Haar type orthonormal wavelet basis having dilation factor A and translation lattice ℤn. They proved that this is the case when the dimension n = 1. This article shows that this is also the case when the dimension n = 2.

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Authors and Affiliations

  1. AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, New Jersey 07974, USA

    Jeffrey C. Lagarias

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

    Yang Wang

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  1. Jeffrey C. Lagarias
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  2. Yang Wang
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Lagarias, J., Wang, Y. Haar Type Orthonormal Wavelet Bases in R2. J Fourier Anal Appl 2, 1–14 (1995). https://doi.org/10.1007/s00041-001-4019-2

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  • DOI: https://doi.org/10.1007/s00041-001-4019-2

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