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Abstract
We study the properties of the continuous measures μ k , induced by the wavelet packet algorithm on the Borel sets of $[0,1)$, in the case of Lemarie–Meyer wavelet. It is still an open problem to determine if these measures are absolutely continuous with respect to the Lebesgue measure. This problem was formulated by Coifman, Meyer and Wickerhauser in [2]. In order to understand if these measures are absolutely continuous or not, it is important to know their Fourier coefficients. We achieve this goal in two steps. First we provide explicit formulas for the values of μ k in dyadic intervals in terms of the wavelet packets, then we show that each μ k is the weak limit of certain probability measures whose Fourier coefficients are easy to calculate.
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