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



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






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


Mat. Sb., 2015, Volume 206, Number 1, Pages 29–38 (Mi msb8435)  

M. Riesz-Schur-type inequalities for entire functions of exponential type

Michael I. Ganzburga, Paul Nevaib, Tamás Erdélyic

a Hampton University
b KAU and Upper Arlington (Columbus), Ohio, USA
c Texas A&M University

Abstract: We prove a general M. Riesz-Schur-type inequality for entire functions of exponential type. If $f$ and $Q$ are two functions of exponential types $\sigma > 0$ and $\tau \ge 0$, respectively, and if $Q$ is real-valued and the real zeros of $Q$, not counting multiplicities, are bounded away from each other, then
$$ |f(x)|\le (\sigma+\tau) (A_{\sigma+\tau}(Q))^{-1/2}\|Q f\|_{\mathrm C(\mathbb R)},\qquad x\in \mathbb R, $$
where
$$ A_s(Q) \stackrel{\mathrm{def}}{=}\inf_{x\in\mathbb R} ([Q'(x)]^2+s^2 [Q(x)]^2). $$
We apply this inequality to the weights $Q(x)\stackrel{\mathrm{def}}{=} \sin (\tau x)$ and $Q(x) \stackrel{\mathrm{def}}{=} x$ and describe the extremal functions in the corresponding inequalities.
Bibliography: 7 titles.

Keywords: M. Riesz-Schur-type inequalities, Duffin-Schaeffer inequality, entire functions of exponential type.

Funding Agency Grant Number
KAU 20-130/1433 HiCi
The research of Paul Nevai was supported by KAU (grant no. 20-130/1433 HiCi).


DOI: https://doi.org/10.4213/sm8435

Full text: PDF file (545 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2015, 206:1, 24–32

Bibliographic databases:

UDC: 517.53
MSC: 41A17, 26D07
Received: 15.04.2014

Citation: Michael I. Ganzburg, Paul Nevai, Tamás Erdélyi, “M. Riesz-Schur-type inequalities for entire functions of exponential type”, Mat. Sb., 206:1 (2015), 29–38; Sb. Math., 206:1 (2015), 24–32

Citation in format AMSBIB
\Bibitem{GanNevErd15}
\by Michael~I.~Ganzburg, Paul~Nevai, Tam\'as~Erd{\'e}lyi
\paper M.~Riesz-Schur-type inequalities for entire functions of exponential type
\jour Mat. Sb.
\yr 2015
\vol 206
\issue 1
\pages 29--38
\mathnet{http://mi.mathnet.ru/msb8435}
\crossref{https://doi.org/10.4213/sm8435}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3354960}
\zmath{https://zbmath.org/?q=an:06439406}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015SbMat.206...24G}
\elib{http://elibrary.ru/item.asp?id=23421596}
\transl
\jour Sb. Math.
\yr 2015
\vol 206
\issue 1
\pages 24--32
\crossref{https://doi.org/10.1070/SM2015v206n01ABEH004444}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000351527000003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925277806}


Linking options:
  • http://mi.mathnet.ru/eng/msb8435
  • https://doi.org/10.4213/sm8435
  • http://mi.mathnet.ru/eng/msb/v206/i1/p29

    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
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:396
    Full text:75
    References:33
    First page:27

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