The Characterization of a Pair of Canonical Frames Generated by Several Compactly Supported Functions
Wavelet analysis has become a popular subject in scientific research during the past twenty years. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonical dual wavelet frame cannot be generated by the translations and dilations of a single function.
J. Q. Wang and J. G. Wang, "The Characterization of a Pair of Canonical Frames Generated by Several Compactly Supported Functions", Key Engineering Materials, Vols. 439-440, pp. 1135-1140, 2010