Band-Limited Wavelets with Subexponential Decay

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.