Some remarks on Boas transforms of wavelets

In this paper, we study Boas transforms of wavelets and obtain a sufficient condition under which the Boas transform of a wavelet is the derivative of another wavelet. Also, a characterization of the Boas transform of a wavelet (Formula presented.) is given. A sufficient condition is given to obtain higher order vanishing moments of Boas transforms of wavelets. Further, we study the Boas transform of wavelets in (Formula presented.). Finally, higher order vanishing moments of Boas transforms of wavelets have been used to approximate finite energy functions.