Vanishing moments of Hilbert transform of wavelets (Q2825731)

Hilbert transform and its basic properties are given in [\textit{G. H. Hardy}, Q. J. Math., Oxf. Ser. 3, 102--112 (1932; Zbl 0004.39201)]. The higher vanishing moments of wavelets under various conditions on \(\Psi(x)\) have been investigated in [\textit{E. Hernández} and \textit{G. Weiss}, A first course on wavelets. Boca Raton, FL: CRC Press (1996; Zbl 0885.42018); \textit{D. F. Walnut}, An introduction to wavelet analysis. Basel: Birkhäuser (2002; Zbl 0989.42014)]. This paper deals with a study of the higher vanishing moments of Hilbert transform of wavelets under certain conditions. The authors follow the definition of Hilbert transform of order n given by \textit{F. W. King} [Hilbert transforms. Volume 1. Cambridge: Cambridge University Press (2009; Zbl 1188.44005)].