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M. Kashiwara, A. Kowata, K. Minemura, K. Okamoto, T. Oshima, M. Tanaka, Eigenfunctions of Invariant Differential Operators on a Symmetric Space, Annals of Mathematics, Second Series, Vol. 107, No. 1 (Jan., 1978), pp. 1-39
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Kashiwara et al. (1978) studied this question.
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