Rao, Murali; Šikić, Hrvoje; Song, Renming Application of Carleson’s theorem to wavelet inversion. (English) Zbl 0816.42018 Control Cybern. 23, No. 4, 761-771 (1994). Inversion formula for continuous wavelet transforms on the real line is proved to be valid pointwise almost everywhere for functions \(f\in L^ p\), \(1< p<\infty\). The related condition for mother wavelets is given in terms of their Fourier transforms.Remark: Close results for \(L^ p\)-functions including convergence of the inversion formula in \(L^ p\)-norm and in a.e.-sense have been obtained by the reviewer and E. Shamir in Integral Equations and Oper. Theory (to appear) and by the reviewer [see “On Calderón’s reproducing formula”, Inst. of Math., Hebrew Univ. of Jerusalem, Preprint No. 15, 1993/94]. According to these papers the condition for wavelet functions can be given just in terms of these functions without using the Fourier transform. Reviewer: B.Rubin (Jerusalem) Cited in 3 ReviewsCited in 9 Documents MSC: 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems Keywords:inversion formula; continuous wavelet transforms; mother wavelets PDFBibTeX XMLCite \textit{M. Rao} et al., Control Cybern. 23, No. 4, 761--771 (1994; Zbl 0816.42018)