Ufa Mathematical Journal
    Volume 5, Number 3, pp. 140-148

    Wiener's theorem for periodic at infinity functions with summable weighted Fourier series

    Strukova I.I.


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    In the article we define a Banach algebra of periodic at infinity functions. For this class of functions we introduce the notions of a Fourier series, its absolute convergence, and invertibility. We obtain an analogue of Wiener's theorem on absolutely convergent Fourier series for periodic at infinity functions whose Fourier coefficients are summable with a weight.