About Nonstationary Multiresolution Analysis and Wavelets

The characterization of orthonormal bases of wavelets by means of convergent series involving only the mother wavelet is known, as well as the characterization of wavelets which can be constructed from a stationary multiresolution analysis or a scaling function (see for example 11] and references therein). Here we show that under some asymptotic condition, these results remain true in the nonstationary case.