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Item A global estimate for the Legendre function for the root systems of type A with arbitrary multiplicities(2008-03-30T23:25:16Z) Sawyer, PatriceWe generalize the global estimate Jean-Philippe Anker found for the Legendre function $\phi_0$ on symmetric spaces of noncompact type to the root systems of type A with arbitrary multiplicities.Item Géométrie hyperbolique pour les non-initié(Acfas-Sudbury, 2004) Sawyer, PatriceItem The inverse of the Abel transform on ${\bf SU}^{\star}(2n)/{\bf Sp}(n)$(2007-09-05T02:24:05Z) Sawyer, PatriceIn this note, we study the inverse of the Abel transform for the symmetric space ${\bf SU}^{\star}(2n)/{\bf Sp}(n)$. We start by giving a recursive formula for the dual of the Abel transform on the root system $A_{n-1}$. This formula allows us to consider a transmutation property on the generalized Abel transform associated to $A_{n-1}$.