RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2012, Volume 92, Issue 2, Pages 302–312 (Mi mz8874)  

Rapid Decrease of Entire Functions along the Real Axis and the Uniqueness of the Fourier-Transform Pair

A. M. Sedletskii

M. V. Lomonosov Moscow State University

Abstract: We study integral classes of entire functions rapidly decreasing along the real axis, i.e., classes of entire functions whose rapid decrease along the real axis is brought about by the existence of definite weighted integrals. We establish a relationship between these classes and some classes known earlier, in which the decrease of functions along the real axis is given by uniform estimates. As an application, we obtain a concrete realization (also in the integral sense) of the well-known Wiener thesis that the “pair $f$ and $\widehat{f}$ cannot be very small at infinity”.

Keywords: integral class of entire functions, rapidly decreasing entire function, Fourier transform, Fourier-transform pair, definite weighted integral, generalized indicator of a function, Young duality of functions

DOI: https://doi.org/10.4213/mzm8874

Full text: PDF file (507 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2012, 92:2, 270–279

Bibliographic databases:

Document Type: Article
UDC: 517.547.22+517.443
Received: 01.09.2010

Citation: A. M. Sedletskii, “Rapid Decrease of Entire Functions along the Real Axis and the Uniqueness of the Fourier-Transform Pair”, Mat. Zametki, 92:2 (2012), 302–312; Math. Notes, 92:2 (2012), 270–279

Citation in format AMSBIB
\Bibitem{Sed12}
\by A.~M.~Sedletskii
\paper Rapid Decrease of Entire Functions along the Real Axis and the Uniqueness of the Fourier-Transform Pair
\jour Mat. Zametki
\yr 2012
\vol 92
\issue 2
\pages 302--312
\mathnet{http://mi.mathnet.ru/mz8874}
\crossref{https://doi.org/10.4213/mzm8874}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3201568}
\zmath{https://zbmath.org/?q=an:06138383}
\elib{http://elibrary.ru/item.asp?id=20731589}
\transl
\jour Math. Notes
\yr 2012
\vol 92
\issue 2
\pages 270--279
\crossref{https://doi.org/10.1134/S0001434612070280}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000308042500028}
\elib{http://elibrary.ru/item.asp?id=20476648}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865771570}


Linking options:
  • http://mi.mathnet.ru/eng/mz8874
  • https://doi.org/10.4213/mzm8874
  • http://mi.mathnet.ru/eng/mz/v92/i2/p302

    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
  • Математические заметки Mathematical Notes
    Number of views:
    This page:322
    Full text:56
    References:41
    First page:40

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