Abstract
L2 harmonic analysis for Dirac spinors on the complex hyperbolic space Hn(C) is developed. The spinor spherical functions are calculated in terms of Jacobi functions. The Plancherel and Paley–Wiener theorems for the spherical transform are obtained by reduction to Jacobi analysis. We demonstrate analytically the existence of harmonic L2 spinors in the case of n even. The action of the invariant differential operators on the Poisson transforms is given explicitly.
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