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Continuous two-scale equations and dyadic wavelets

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Abstract

The objective of this paper is to investigate the solvability of a continuous two-scale (or refinement) equation and to characterize the solutions of the equation. In addition, the notion of continuous multiresolution analysis (or approximation), CMRA, generated by such a solution is introduced. Here, the notion of continuity follows from a standard engineering terminology, meaning that continuous-time instead of discretetime considerations are studied. This solution, also called a scalling function of the CMRA, gives rise to some dyadic wavelet, a notion introduced by Mallat and Zhong, for multilevel signal decompositions.

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Author notes

  1. Xianliang Shi

    Present address: Department of Mathematics, Hangzhou University, Hangzhou, PR China

Authors and Affiliations

  1. Center for Approximation Theory, Department of Mathematics, Texas A&M University, 77843, College Station, TX, USA

    Charles K. Chui & Xianliang Shi

Authors
  1. Charles K. Chui
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  2. Xianliang Shi
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Additional information

This research was supported by NSF Grant DMS-92-06928, ARO Contract DAAL 03-90-G0091, and Texas Coordinating Board of Higher Education Grant ATP 999903-054.

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Chui, C.K., Shi, X. Continuous two-scale equations and dyadic wavelets. Adv Comput Math 2, 185–213 (1994). https://doi.org/10.1007/BF02521107

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  • DOI: https://doi.org/10.1007/BF02521107

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