Super-wavelets and deeomposable wavelet frames
Abbreviated Journal Title
J. Fourier Anal. Appl.
wavelet; super-wavelet; decomposable and extendable Parseval wavelet; frames; Mathematics, Applied
A wavelet frame is called decomposable whenever it is equivalent to a super-wavelet frame of length greater than one. Decomposable wavelet frames are closely related to some problems on super-wavelets. In this article we first obtain some necessary or sufficient conditions for decomposable Parseval wavelet frames. As an application of these conditions, we prove that for each n > 1 there exists a Parseval wavelet frame which is m-decomposable for any 1 < m < n, but not k-decomposable for any k > n. Moreover; there exists a super-wavelet whose components are non-decomposable. Similarly we also prove that for each n > 1, there exists a Parseval wavelet frame that can be extended to a super-wavelet of length m for any 1 < m <= n, but can not be extended to any super-wavelet of length k with k > n. The connection between decomposable Parseval wavelet frames and super-wavelets is investigated, and some necessary or sufficient conditions for extendable Parseval wavelet frames are given.
Journal of Fourier Analysis and Applications
"Super-wavelets and deeomposable wavelet frames" (2005). Faculty Bibliography 2000s. 5232.