Algebras of Almost Periodic Functions with Bohr-fourier Spectrum in a Semigroup: Hermite Property and Its Applications
نویسنده
چکیده
It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener–Hopf type of rectangular matrix functions and the Toeplitz corona problem in the context of almost periodic functions of several variables.
منابع مشابه
The bass and topological stable ranks for algebras of almost periodic functions on the real line
Let Λ be a sub-semigroup of the reals. We show that the Bass and topological stable ranks of the algebras APΛ = {f ∈ AP : σ(f) ⊆ Λ} of almost periodic functions on the real line and with Bohr spectrum in Λ are infinite whenever the algebraic dimension of the Q-vector space generated by Λ is infinite. This extends Suárez’s result for APR = AP. Also considered are general subalgebras of AP. Intro...
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