International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 1, Article ID 86238, 26 pages
doi:10.1155/IJMMS/2006/86238
Inversion formulas for Riemann-Liouville transform and its dual associated with singular partial differential operators
C. Baccar
, N.B. Hamadi
and L.T. Rachdi
Department of Mathematics, Faculty of Sciences of Tunis, University Tunis El Manar, 2092 Tunis, Tunisia
Abstract
We define Riemann-Liouville transform ℛα and its dual tℛα associated with two singular partial differential operators. We establish some results of harmonic analysis for the Fourier transform connected with ℛα. Next, we prove inversion formulas for the operators ℛα, tℛα and a Plancherel theorem for tℛα.