Band-limited wavelets beyond Gevrey regularity (Q6591743)

The authors design a family of Meyer-type orthonormal wavelets. More precisely, the wavelet \(\psi\) is band-limited and space concentrated \N\[\N \left|\psi(x)\right| \leq C e^{-h \left(\ln ^2 |x|\right)/ W\left(\ln |x|\right)}, \qquad h>0,\N\]\Nwhere \(W\) is the restriction of the principal branch of the Lambert function on \((0,\infty)\). The Lambert function is the inverse to \(z e^z.\) The wavelets are defined via explicit expression for the Fourier transform \(\widehat{\psi}\), which belongs to extended Gevrey classes. The constructed family gives a new example of band-limited wavelets with subexponential decay.