Singularities of Jacobi series on C2 and the Poisson process equation

A classical theorem of Gabor Szego relates the singularities of real zonal harmonic expansions with those of associated analytic functions of a single complex variable. Zeev Nehari developed the counterpart for Legendre series on the C-plane by generalizing Szego's theorem. This paper function theretically identifies the singularities of analytic symmetric Jacobi series on C² with those of analytic functions on the C-plane. One feature is that information about the singularities of solutions of Solomon Bochner's Poisson process equation flow from the expansion coefficients. Others are that the Szego and Nehari theorems appear on characteristic subspaces. And, that this PDE, unlike those normally encountered in function theory, is hyperbolic in the real domain.