This paper indicates how to find energy moments in direct and Fourier space of a solution to the functional equation u(x) = ∑k = 0N - 1 2cₖ u(2x - k) and shows that the Sobolev regularity of u is determined by the spectral radius of a matrix defined from the coefficients (cₖ ). The results are applied to compactly supported orthonormal wavelets.
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Lars Villemoes (1992) studied this question.
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