Band-limited wavelets beyond Gevrey regularity
Nenad Teofanov, Filip Tomić, Stefan Tutić · International Journal of Wavelets Multiresolution and Information Processing · 2024
It is known that a smooth function of exponential decay at infinity cannot be an orthonormal wavelet. Dziubański and Hernández constructed smooth orthonormal wavelets of Gevrey-type subexponential decay. We weaken the Gevrey-type decay and construct orthonormal wavelets of subexponential decay related to the so-called extended Gevrey classes. The virtue of our construction is that precise asymptotics of functions from such classes can be given in terms of the Lambert [Formula: see text]-function.