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Characterising the Accuracy of Multivariable Refinable Functions via the Symbol Function

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Abstract

Suppose that f(x) = (f 1(x),...,f r (x))T, x∈R d is a vector-valued function satisfying the refinement equation f(x) = ∑Λ c κ f(2x−κ) with finite set Λ of Z d and some r×r matricex c κ. The requirements for f to have accuracy p are given in terms of the symbol function m(ξ).

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References

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Authors and Affiliations

  1. School of Mathematics and Computer Sciences, Hubei University, Wuhan, 430062, P. R. China

    Qiu Hui Sheng

  2. Institute of Mathematics, Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100080, P. R. China

    Qiu Hui Sheng

  3. Institute of Mathematics, Academia Sinica, Beijing 100080, P. R. China

    Han Lin Chen

Authors
  1. Qiu Hui Sheng
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  2. Han Lin Chen
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Correspondence to Qiu Hui Sheng.

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Sheng, Q.H., Chen, H.L. Characterising the Accuracy of Multivariable Refinable Functions via the Symbol Function. Acta Math Sinica 17, 277–286 (2001). https://doi.org/10.1007/s101149900014

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  • DOI: https://doi.org/10.1007/s101149900014

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