Abstract:
In this article banach algebra of periodic at infinity functions is defined. For this class of functions notions of Fourier series and absolutely convergent Fourier series are introduced. As a result Wiener's theorem analog devoted to absolutely convergent Fourier series for periodic at infinity functions was proved.
Key words:Banach space, slowly varying at infinity functions, periodic at infinity functions, Wiener's theorem, absolutely convergent Fourier series, invertibility.