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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2014, Volume 14, Issue 1, Pages 98–111 (Mi vngu329)  

This article is cited in 2 scientific papers (total in 2 papers)

Harmonic Analysis of Periodic Vectors and Periodic at Infinity Functions

I. I. Strukova

Voronezh State University

Abstract: In this paper we study vector-valued slowly varying and periodic at infinity functions of several variables. We introduce the notion of Fourier series and derive an analog of the celebrated Wiener theorem that deals with the absolutely convergent Fourier series. We also derive a criterion of representability of periodic at infinity function as a sum of pure periodic and vanishing at infinity functions and criteria of periodicity at infinity for solutions of difference and differential equations. The main results are derived by means of the spectral theory of isometric group representations.

Keywords: Banach space, Banach algebra, slowly varying at infinity functions, periodic at infinity functions, Fourier series, periodic vector, Wiener theorem.

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English version:
Journal of Mathematical Sciences, 2015, 211:6, 874–885

Document Type: Article
UDC: 517.9
Received: 19.09.2013

Citation: I. I. Strukova, “Harmonic Analysis of Periodic Vectors and Periodic at Infinity Functions”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 14:1 (2014), 98–111; J. Math. Sci., 211:6 (2015), 874–885

Citation in format AMSBIB
\Bibitem{Str14}
\by I.~I.~Strukova
\paper Harmonic Analysis of Periodic Vectors and Periodic at Infinity Functions
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2014
\vol 14
\issue 1
\pages 98--111
\mathnet{http://mi.mathnet.ru/vngu329}
\transl
\jour J. Math. Sci.
\yr 2015
\vol 211
\issue 6
\pages 874--885
\crossref{https://doi.org/10.1007/s10958-015-2641-9}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. I. Strukova, “On Wiener's Theorem for functions periodic at infinity”, Siberian Math. J., 57:1 (2016), 145–154  mathnet  crossref  crossref  mathscinet  isi  elib
    2. I. I. Strukova, “Garmonicheskii analiz periodicheskikh na beskonechnosti funktsii v prostranstvakh Stepanova”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 17:2 (2017), 172–182  mathnet  crossref  elib
  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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