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

• Autores: Khalifa Trimèche
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 47, Fasc. 3, 1996, págs. 231-268
• Idioma: inglés
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• Resumen

  • 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 $\mathcal{A}^\ast$.