Green's function-based wavelets: Selected properties
Alireza R. Baghai-Wadji, G.G. Walter · 2002
In this paper we prove the orthogonality of the wavelet functions constructed from the Laplace operator. Using Plancherel's theorem the orthogonality is shown in the wavenumber domain rather than in the real space. The presented analysis is semi-rigorous, since the involved ln|x| function is not in L/sup 2/(R). The wavelet itself is, however, in L/sup 2/(R). A more comprehensive theory will be presented elsewhere. Furthermore, the existence of a large family of wavelet-like orthogonal systems related to the wavelet of the Laplace operator has been shown.