Generalized Wavelets and Generalized Continuous Wavelet Transforms on Semisimple Lie Groups and on Cartan Motion Groups

The classical continuous wavelet transform and its Plancherel and inversion formulas admit a group theoretic interpretation in connection with the ax + b group (the group of affine transformations of the real line), the Heisenberg group and in greater generality with locally compact group admitting square integrable representations (see [62] [63] [81] [119].) Also classical continuous multiscale analysis admits a group theoretic interpretation in connection with the ax + b group (see [119]). But the case of semisimple Lie groups has not be considered.