Characterizing bounded orthogonally additive polynomials on vector lattices

We derive formulas for characterizing bounded orthogonally additive polynomials in two ways. Firstly, we prove that certain formulas for orthogonally additive polynomials derived in Kusraeva (Vladikavkaz Math J 16(4):49–53, 2014) actually characterize them. Secondly, by employing complexifications of the unique symmetric multilinear maps associated with orthogonally additive polynomials, we derive new characterizing formulas.