Revista Matemática Iberoamericana
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Published online: 1996-08-31
A new technique to estimate the regularity of refinable functionsAlbert Cohen and Ingrid Daubechies (1) Université Pierre et Marie Curie, Paris, France
(2) Duke University, Durham, USA
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 Albert, Daubechies Ingrid: A new technique to estimate the regularity of refinable functions. Rev. Mat. Iberoam. 12 (1996), 527-591. doi: 10.4171/RMI/207