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Base d’ondelettes sur les groupes de Lie stratifiés. (Basis of ondelettes on stratified Lie groups). (French) Zbl 0711.43004
The author generalizes the theory of ondelettes, started by Meyer and Grossmann for \({\mathbb{R}}^ n\) to general stratified nilpotent Lie groups G, constructing a hilbertian basis of \(L^ 2(G)\) formed with regular and oscillating functions, “uniformly” localized in space and frequency (as in the ondelettes theory). On certain groups this basis is composed of finitely many functions and the functions obtained from them by “dyadic” dilations-translations. The way of constructing this basis lies in a multi-scale analysis composed from generalized spline-surfaces spaces.
Reviewer: H.Rindler

MSC:
43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
22E25 Nilpotent and solvable Lie groups
42C15 General harmonic expansions, frames
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