Generalized Wavelets And Generalized Continuous Wavelet Transforms on Hypergroups

A continuous wavelet transform for functions on ℝ ⁿ is an integral transform for which the kernel is the dilated translate of a so-called wavelet g, a quite arbitrary square integrable function on ℝ ⁿ. A Plancherel formula for this transform is obtained, and in the course of its derivation we naturally arrive at an admissibility assumption for the wavelet g. There follow a Parseval and an inversion formula.