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Abstract. We consider polynomials P in additive functions gi,... ,g m and present two approaches for a characterization of those generalized polynomials p, which may beUnder rather general assumptions on the domains of the gi and of P, one of the approaches is based on certain properties of subspaces generated by translates of p. The other approach utilizes the fact, that every p is the diagonalization of an associated multi-Jensen function.

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