Exceptional sets and wavelet packets orthonormal bases

We give a partial positive answer to a problem posed by Coifman et al. in 1]. Indeed, starting from the transfer function m₀ arising from the Meyer wavelet and assuming m₀=1 only on –/3, /3], we provide an example of pairwise disjoint dyadic intervals of the form I(n, q)=2^qn, 2^q(n+1)), (n, q)EN×Z, which cover 0, +) except for a set A of Hausdorff dimension equal to 1/2, and such that the corresponding wavelet packets 2^q/2w_n (2^qx–k), kZ, (n, q)EN×Z form an orthonormal basis of L²(R).