Revista Matemática Iberoamericana


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Volume 12, Issue 2, 1996, pp. 527–591
DOI: 10.4171/RMI/207

A new technique to estimate the regularity of refinable functions

Albert Cohen[1] and Ingrid Daubechies[2]

(1) Laboratoire J.L. Lions, Université Pierre et Marie Curie, 175 rue du Chevaleret, 75013, PARIS, FRANCE
(2) Department of Mathematics, Duke University, P.O. Box 90320, NC 27708-0320, DURHAM, UNITED STATES

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.

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Cohen A, Daubechies I. A new technique to estimate the regularity of refinable functions. Rev. Mat. Iberoamericana 12 (1996), 527-591. doi: 10.4171/RMI/207