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It is proved that the unital Banach algebra of almost periodic functions ofseveral variables with Bohr-Fourier spectrum in a given additive semigroup isan Hermite ring. The same property holds for the Wiener algebra of functionsthat in addition have absolutely convergent Bohr-Fourier series. Asapplications of the Hermite property of these algebras, we study factorizationsof Wiener--Hopf type of rectangular matrix functions and the Toeplitz coronaproblem in the context of almost periodic functions of several variables.

Algebras of Almost Periodic Functions with Bohr-Fourier Spectrum in a Semigroup: Hermite Property and its Applications