Extension of local positive definite $\mathbb{Z}_{2}^{n}$-superfunctions

By defining a concept of boundedness for $\mathbb{Z}_2^n$-superfunction, we show that each local positive definite $\mathbb{Z}_2^n$-superfunctions, which is bounded in some sense, on a $\mathbb{Z}_2^n$-Lie supergroup has a positive definite extension to all of the $\mathbb{Z}_{2}^{n}$-Lie supergroup.

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