AbstractLetPkc(G) denote the set of continuous functions withknegative squares on a locally compact commutative groupG.Every functionfϵPkc(G) is definitizable in the sense thatis positive definite for certain complex measures ω onGwith finite support [9]. The proof of this fact was base on a result of M. A. Naimark about common nonpositive eigenvectors of commuting unitary operators in a Pontrjagin space. It is the aim of this note to prove without any use of the theory of Pontrjagin spaces the definitizability of functionsfϵPkc(G) which are of polynomial growth. In Section 3 we show, how the definitizability of functionsfϵPkc(G) can be used to prove the existence of common non‐positive eigenvectors of commuting unitary operators in a Pontrjagin