The Paley-Wiener Theorem for the Jacobi Transform and the Local Huygens' Principle for Root Systems with Even Multiplicities

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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.