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In this work we define and study wavelets and continuous wavelet transform on semisimple Lie groups G of real rank l. We prove for this transform Plancherel and inversion formulas. Next using the Abel transform A on G and its dual A*, we give relations between the continuous wavelet transform on G and the classical continuous wavelet transform on Rl, and we deduce the formulas which give the inverse operators of the operators A and A*.
Dans son livre [H. Stein, Ann. of Math. Studies, 63, Princeton Univ. Press, (1970)] E. Stein associe à tout opérateur de Sturm-Liouville la -fonction de Littlewood-Paley et conjecture que, pour tout dans l’intervalle , il existe deux constantes et telles que :
On démontre ces inégalités pour une classe d’opérateurs différentiels singuliers sur et on énonce alors un résultat sur les multiplicateurs concernant ces opérateurs.
In this work we consider two partial differential operators, define a generalized Radon transform and its dual associated with these operators and characterize its range.
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