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The Paley-Wiener theorem for the Jacobi transform and the local Huygens’ principle for root systems with even multiplicities. (English) Zbl 1168.43302
Summary: This note is a continuation of the previous paper by same authors [Indag. Math., New Ser. 16, No. 3-4, 393–428 (2005; Zbl 1113.53034)]. 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.

MSC:
43A85 Harmonic analysis on homogeneous spaces
22E30 Analysis on real and complex Lie groups
33C52 Orthogonal polynomials and functions associated with root systems
33C67 Hypergeometric functions associated with root systems
33C80 Connections of hypergeometric functions with groups and algebras, and related topics
35L05 Wave equation
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References:
[1] Branson, T.; Ólafsson, G.; Pasquale, A., The Paley-Wiener theorem and the local Huygens’ principle for compact symmetric spaces: the even multiplicity case, Indag. math., 16, (2005), this issue · Zbl 1113.53034
[2] Heckman, G.; Schlichtkrull, H., Harmonic analysis and special functions on symmetric spaces, (1994), Academic Press · Zbl 0836.43001
[3] Ólafsson, G.; Pasquale, A., A Paley-Wiener theorem for the θ-hypergeometric transform: the even multiplicity case, J. math. pures appl., 83, 869-927, (2004) · Zbl 1058.33015
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