Study of Periodic Frames and Trivariate Tight Wavelet Frames and Applications in Materials Engineering

摘要

It is shown that there exists a frame wavelet with fast decay in the time domain and compact support in the frequency domain generating a wavelet system whose canonical dual frame cannot be generated by an arbitrary number of generators. A nice approach for constructing three-variable biorthogonal wavelet bundles is developed. The biorthogonality property of three -variable wavelet bundles is discussed. 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.