Duality theorems in the Hermitian setting

In this paper we prove the Poincaré Lemma for circulant matrices with C ∞ entries and the Mittag–Leffler theorem for Hermitian monogenic matrix functions. We then prove algebraic and topological duality theorems for Hermitian monogenic matrix functions. Finally, we use one of these duality theorems to characterize the C 2 n -module H ( K ) ′ , where H denotes the sheaf of Hermitian monogenic functions. These results extend and clarify those obtained in R. Abreu-Blaya et al. (2012) [1].