JournalsrmiVol. 12, No. 2pp. 527–591

A new technique to estimate the regularity of refinable functions

  • Albert Cohen

    Université Pierre et Marie Curie, Paris, France
  • Ingrid Daubechies

    Duke University, Durham, USA
A new technique to estimate the regularity of refinable functions cover
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Abstract

We study the regularity of refinable functions by analyzing the spectral properties of special operators associated to the refinement equation; in particular, we use the Fredholm determinant theory to derive numerical estimates for the spectral radius of these operators in certain spaces. This new technique is particularly useful for estimating the regularity in the cases where the refinement equation has an infinite number of nonzero coefficients and in the multidimensional cases.

Cite this article

Albert Cohen, Ingrid Daubechies, A new technique to estimate the regularity of refinable functions. Rev. Mat. Iberoam. 12 (1996), no. 2, pp. 527–591

DOI 10.4171/RMI/207