Resumen de Continuous wavelet transform on semisimple Lie groups and inversion of the Abel transform and its dual

Khalifa Trimèche

• In this work we define and study wavelets and continuous wavelet transform on semisimple Lie groups $G$ of real rank $\ell$. We prove for this transform Plancherel and inversion formulas. Next using the Abel transform $\mathcal{A}$ on $G$ and its dual $\mathcal{A}^\ast$, we give relations between the continuous wavelet transform on $G$ and the classical continuous wavelet transform on $\mathbb{R}^\ell$, and we deduce the formulas which give the inverse operators of the operators $\mathcal{A}$ and $\mathcal{A}^\ast$.