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We give a characterization of uniqueness of finite rank Fourier-type minimal extensions in \(L_1\)-norm. This generalizes the main result obtained by Lewicki (Proceedings of the Fifth International Conference on Function Spaces, Lecture Notes in Pure and Applied Mathematics, vol. 213, pp. 337–345, 1998) to the case of \(n\)-circular sets in \(\mathbb{C }^n\).

Uniqueness of minimal Fourier-type extensions in $$L_1$$ -spaces