Abstract
AbstractIt is well known that the compactly supported wavelets cannot belong to the class . This is also true for wavelets with exponential decay. We show that one can construct wavelets in the class that are “almost” of exponential decay and, moreover, they are band-limited. We do this by showing that we can adapt the construction of the Lemarié-Meyer wavelets [LM] that is found in [BSW] so that we obtain band-limited, C∞-wavelets on R that have subexponential decay, that is, for every 0 < ε < 1, there exits Cε > 0 such that . Moreover, all of its derivatives have also subexponential decay. The proof is constructive and uses the Gevrey classes of functions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.