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

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

2008-04-11

arxiv.org/abs/0804.1945v1

Mathematics

Functional Analysis

18 pages

Scientific paper

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.

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