Asymptotic Property of Dual Frames of a Wavelet Frame Yielded by Several Refinable Functions

摘要

Wavelet tight frames have attracted more and more attention. In this paper, we show that there exist wavelet frames generated by two functions which have good dual wavelet frames, but for which the standard dual wavelet frame does not consist of wavelets. That is to say, the standard dual wavelet frame cannot be generated by the translations and dilations of a single function.