Abstract
Under very minimal regularity assumptions, it can be shown that 2n−1 functions are needed to generate an orthonormal wavelet basis for L2(ℝn). In a recent paper by Dai et al. it is shown, by abstract means, that there exist subsets K of ℝn such that the single function ψ, defined by $$\hat \psi = \chi K$$ , is an orthonormal wavelet for L2(ℝn). Here we provide methods for construucting explicit examples of these sets. Moreover, we demonstrate that these wavelets do not behave like their one-dimensional couterparts.
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.
