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We explicitly compute the Green's function of the spinor Klein-Gordonequation on the Riemannian and Lorentzian manifolds of the form $M_0 \times ...\times M_N$, with each factor being a space of constant sectional curvature.Our approach is based on an extension of the method of spherical means to thecase of spinor fields and on the use of Riesz distributions.

Spinor Green's functions via spherical means on products of space forms