RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Eurasian Math. J.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Eurasian Math. J., 2016, Volume 7, Number 4, Pages 9–29 (Mi emj238)  

This article is cited in 3 scientific papers (total in 3 papers)

Harmonic analysis of functions periodic at infinity

A. Baskakov, I. Strukova

Faculty of Applied Mathematics, Mechanics and Informatics, Voronezh State University, 1 Universitetskaya Sq, 394036 Voronezh, Russia

Abstract: In this paper we introduce the notion of vector-valued functions periodic at infinity. We characterize the sums of the usual periodic functions and functions vanishing at infinity as a subclass of these functions. Our main focus is the development of the basic harmonic analysis for functions periodic at infinity and an analogue of the celebrated Wienerís Lemma that deals with absolutely convergent Fourier series. We also derive criteria of periodicity at infinity for solutions of difference and differential equations. Some of the results are derived by means of the spectral theory of isometric group representations.

Keywords and phrases: Banach space, functions slowly varying at infinity, functions periodic at infinity, Wiener's theorem, absolutely convergent Fourier series, invertibility, difference equations.

Funding Agency Grant Number
Russian Science Foundation 14-21-00066
Russian Foundation for Basic Research 16-01-00197_a
The results of Section 5 were obtained with support of the Russian Science Foundation, project no. 14-21-00066 in the Voronezh State University. The other results were obtained with support of the Russian Foundation for Basic Research, project no. 16-01-00197 in the Voronezh State University.


Full text: PDF file (451 kB)
References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 34A55, 34B05, 58C40
Received: 14.03.2016
Language: English

Citation: A. Baskakov, I. Strukova, “Harmonic analysis of functions periodic at infinity”, Eurasian Math. J., 7:4 (2016), 9–29

Citation in format AMSBIB
\Bibitem{BasStr16}
\by A.~Baskakov, I.~Strukova
\paper Harmonic analysis of functions periodic at infinity
\jour Eurasian Math. J.
\yr 2016
\vol 7
\issue 4
\pages 9--29
\mathnet{http://mi.mathnet.ru/emj238}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000398292700001}


Linking options:
  • http://mi.mathnet.ru/eng/emj238
  • http://mi.mathnet.ru/eng/emj/v7/i4/p9

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, “Garmonicheskii analiz periodicheskikh na beskonechnosti funktsii v odnorodnykh prostranstvakh”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 2(39), 29–38  mathnet  crossref
    2. A. G. Baskakov, I. I. Strukova, I. A. Trishina, “Solutions almost periodic at infinity to differential equations with unbounded operator coefficients”, Siberian Math. J., 59:2 (2018), 231–242  mathnet  crossref  crossref  isi  elib
    3. A. G. Baskakov, V. E. Strukov, I. I. Strukova, “On the almost periodic at infinity functions from homogeneous spaces”, Probl. anal. Issues Anal., 7(25):2 (2018), 3–19  mathnet  crossref
  • Eurasian Mathematical Journal
    Number of views:
    This page:459
    Full text:234
    References:50

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019