The Paley-Wiener theorem for the Jacobi transform and the local Huygens' principle for root systems with even multiplicities

This note is a continuation of the previous paper by same authors [this issue]. Its purpose is to extend the results to the context of root systems with even multiplicities. Under the even multiplicity assumption, we prove a local Paley-Wiener theorem for the Jacobi transform and the strong Huygens' principle for the wave equation associated with the modified compact Laplace operator.