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






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


Mat. Zametki, 2015, Volume 98, Issue 5, Pages 684–694 (Mi mz10894)  

This article is cited in 1 scientific paper (total in 1 paper)

On the Sharpness of Jackson's Inequality in the Spaces $L_p$ on the Half-Line with Power Weight

V. I. Ivanov

Tula State University

Abstract: In the space $L_p$, $1\leq p<2$, on the half-line with power weight, Jackson's inequality between the value of the best approximation of a function by even entire functions of exponential type and its modulus of continuity defined by means of a generalized shift operator is well known. The question of the sharpness of the inequality remained open. For the constant in Jackson's inequality, we obtain a lower bound, which proves its sharpness.

Keywords: Jackson's inequality, value of the best approximation, the space $L_p$, $1\leq p<2$, entire functions of exponential type, modulus of continuity, generalized shift operator, substochastic matrix, Hoeffding estimate.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00045
Ministry of Education and Science of the Russian Federation 1.1333.2014К


DOI: https://doi.org/10.4213/mzm10894

Full text: PDF file (488 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2015, 98:5, 742–751

Bibliographic databases:

UDC: 517.5
Received: 08.05.2015

Citation: V. I. Ivanov, “On the Sharpness of Jackson's Inequality in the Spaces $L_p$ on the Half-Line with Power Weight”, Mat. Zametki, 98:5 (2015), 684–694; Math. Notes, 98:5 (2015), 742–751

Citation in format AMSBIB
\Bibitem{Iva15}
\by V.~I.~Ivanov
\paper On the Sharpness of Jackson's Inequality in the Spaces~$L_p$ on the Half-Line with Power Weight
\jour Mat. Zametki
\yr 2015
\vol 98
\issue 5
\pages 684--694
\mathnet{http://mi.mathnet.ru/mz10894}
\crossref{https://doi.org/10.4213/mzm10894}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3438524}
\elib{http://elibrary.ru/item.asp?id=24850205}
\transl
\jour Math. Notes
\yr 2015
\vol 98
\issue 5
\pages 742--751
\crossref{https://doi.org/10.1134/S0001434615110048}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000369701000004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84953333489}


Linking options:
  • http://mi.mathnet.ru/eng/mz10894
  • https://doi.org/10.4213/mzm10894
  • http://mi.mathnet.ru/eng/mz/v98/i5/p684

    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. D. V. Gorbachev, V. I. Ivanov, “Tochnoe neravenstvo Dzheksona v $L_p(\mathbb R^d)$ s vesom Danklya”, Matem. zametki, 105:5 (2019), 666–684  mathnet  crossref  elib
  • Математические заметки Mathematical Notes
    Number of views:
    This page:418
    Full text:50
    References:53
    First page:48

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