  This note is a continuation of the previous paper math.AP/0411383 by the same
authors. Its purpose is to extend the results of math.AP/0411383 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.
