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Analysis and Construction of Multivariate Interpolating Refinable Function Vectors

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Abstract

In this paper, we shall introduce and study a family of multivariate interpolating refinable function vectors with some prescribed interpolation property. Such interpolating refinable function vectors are of interest in approximation theory, sampling theorems, and wavelet analysis. In this paper, we characterize a multivariate interpolating refinable function vector in terms of its mask and analyze the underlying sum rule structure of its generalized interpolatory matrix mask. We also discuss the symmetry property of multivariate interpolating refinable function vectors. Based on these results, we construct a family of univariate generalized interpolatory matrix masks with increasing orders of sum rules and with symmetry for interpolating refinable function vectors. Such a family includes several known important families of univariate refinable function vectors as special cases. Several examples of bivariate interpolating refinable function vectors with symmetry will also be presented.

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

    Bin Han & Xiaosheng Zhuang

Authors
  1. Bin Han
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  2. Xiaosheng Zhuang
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Correspondence to Bin Han.

Additional information

Research was supported in part by NSERC Canada under Grant RGP 228051.

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Han, B., Zhuang, X. Analysis and Construction of Multivariate Interpolating Refinable Function Vectors. Acta Appl Math 107, 143–171 (2009). https://doi.org/10.1007/s10440-008-9399-8

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  • DOI: https://doi.org/10.1007/s10440-008-9399-8

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