RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Sib. J. Pure and Appl. Math.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (282 kB)
References: PDF file   HTML file

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

Document Type: Article
UDC: 517.9

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} 

• http://mi.mathnet.ru/eng/vngu329
• http://mi.mathnet.ru/eng/vngu/v14/i1/p98

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
•  Number of views: This page: 141 Full text: 20 References: 26 First page: 12