The group SU(1,d) acts naturally on the Hilbert space L²(B dμ_α) (α > -1), where B is the unit ball of ℂᵈ and dμ_α the weighted measure (1-|z|²)^α dm(z). It is proved that the irreducible decomposition of the space has finitely many discrete part
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Genkai Zhang (1992) studied this question.
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