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Harmonic Analysis of Periodic Vectors and Functions Periodic at Infinity

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We study vector-valued slowly varying and periodic at infinity functions of several variables. We prove a counterpart of the Wiener theorem on absolutely converging Fourier series. We establish a criterion for representation of periodic at infinity functions as the sum of periodic functions and functions converging to zero and a criterion of periodicity at infinity for solutions to difference and differential equations. Bibliography: 18 titles.

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References

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  1. Voronezh State University, 1, Universitetskaya pl., Voronezh, 394036, Russia

    I. I. Strukova

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  1. I. I. Strukova
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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 14, No. 1, 2014, pp. 98-111.

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Strukova, I.I. Harmonic Analysis of Periodic Vectors and Functions Periodic at Infinity. J Math Sci 211, 874–885 (2015). https://doi.org/10.1007/s10958-015-2641-9

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