Abstract
In order to provide a unified treatment for the continuum and digital realm of multivariate data, Guo, Labate, Weiss and Wilson [Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 78-87] introduced the notion of AB-wavelets in the context of multiscale analysis. We continue and extend their work by studying the frame properties of AB-wavelet systems {DADBTk??(k ? Zn; 1 <? ? <? L)}in L2(Rn). More precisely, we establish four theorems giving su_cient conditions under which the AB-wavelet system constitutes a frame for L2(Rn). The proposed conditions are stated in terms of the Fourier transforms of the generating functions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
