Green´s function-based wavelets: Selected properties

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 L²(R). The wavelet itself is, however, in L²(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