RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
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



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 5, Pages 205–224 (Mi izv2817)  

Canonical products generated by perturbations of the sequence of integers, and their asymptotic estimation

A. A. Yukhimenko

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We obtain asymptotic estimates for canonical products with complex zeros of the form $\lambda_n=n+o(n)$. A formula is found for the excess of the system of exponentials $\{e^{i\lambda_nt}\}_{n\in\mathbb{Z}}$ in the space $L^2(-\pi,\pi)$. We consider some particular cases of sequences $\{\lambda_n\}_{n\in\mathbb{Z}}$.

Keywords: canonical product, asymptotic estimate, slowly varying function, excess of a system.

DOI: https://doi.org/10.4213/im2817

Full text: PDF file (544 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2010, 74:5, 1083–1101

Bibliographic databases:

UDC: 517.547.2+517.538.2
MSC: 30D15, 30E15, 30B60
Received: 20.06.2008
Revised: 28.07.2009

Citation: A. A. Yukhimenko, “Canonical products generated by perturbations of the sequence of integers, and their asymptotic estimation”, Izv. RAN. Ser. Mat., 74:5 (2010), 205–224; Izv. Math., 74:5 (2010), 1083–1101

Citation in format AMSBIB
\Bibitem{Yuk10}
\by A.~A.~Yukhimenko
\paper Canonical products generated by perturbations of the sequence of integers, and their asymptotic estimation
\jour Izv. RAN. Ser. Mat.
\yr 2010
\vol 74
\issue 5
\pages 205--224
\mathnet{http://mi.mathnet.ru/izv2817}
\crossref{https://doi.org/10.4213/im2817}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2757906}
\zmath{https://zbmath.org/?q=an:1203.30026}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2010IzMat..74.1083Y}
\elib{http://elibrary.ru/item.asp?id=20358767}
\transl
\jour Izv. Math.
\yr 2010
\vol 74
\issue 5
\pages 1083--1101
\crossref{https://doi.org/10.1070/IM2010v074n05ABEH002517}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000285022600007}
\elib{http://elibrary.ru/item.asp?id=16977328}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78049351179}


Linking options:
  • http://mi.mathnet.ru/eng/izv2817
  • https://doi.org/10.4213/im2817
  • http://mi.mathnet.ru/eng/izv/v74/i5/p205

    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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:367
    Full text:89
    References:25
    First page:11

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