Frame wavelet sets in Rd

  • Authors:

  • X. Dai;Y. Diao;Q. Gu;D. Han

  • Affiliations:

  • Department of Mathematics, University of North Carolina at Charlotte, Charlotte, NC;Department of Mathematics, University of North Carolina at Charlotte, Charlotte, NC;Department of Mathematics, East China Normal University, Shanghai, China;Department of Mathematics, University of Central Florida, Orlando, FL

  • Venue:
  • Journal of Computational and Applied Mathematics - Special issue: Approximation theory, wavelets, and numerical analysis
  • Year:
  • 2003

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Abstract

In this paper, we discuss the characterization of frame wavelet sets. We extend some results obtained earlier in the one-dimensional case. More specifically, we completely characterize tight frame wavelet sets in higher dimensions and obtain some necessary conditions and sufficient conditions for a set E to be a frame wavelet set in Rd. Several examples are presented and compared with those in the one-dimensional case. Using our results, one can easily construct various frame wavelet sets.