Article
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.
DOI:10.13108/2013-5-3-140
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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.