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.
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Teofanov et al. (2024) studied this question.
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