Clifford-Hermite wavelets in Euclidean space
The continuous wavelet transform analyzes the distribution of a function in both space and scale using a wavelet function phi. Many choices of phi are possible; one example is the Marr wavelets, obtained by applying some power of the Laplacian to a Gaussian. In this paper these wavelets are generalized to Clifford-valued wavelets by applying some power of the Dirac operator to the Gaussian, thus obtaining Gaussians weighted by Hermite polynomials. Just as the family of scaled Gaussians obey the heat equation, the scaled Clifford-valued wavelets also obey a certain PDE which is worked out explicitly.
scientific article; zbMATH DE number 1445613