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, 1997, Volume 62, Issue 3, Pages 332–342 (Mi mz1615)  

This article is cited in 4 scientific papers (total in 4 papers)

An extremal problem for algebraic polynomials with zero mean value on an interval

V. V. Arestov, V. Yu. Raevskaya

Ural State University

Abstract: Let $\mathscr P_n^0(h)$ be the set of algebraic polynomials of degree $n$ with real coefficients and with zero mean value (with weight $h$) on the interval $[-1,1]$:
$$ \int_{-1}^1h(x)p_n(x)dx=0; $$
here $h$ is a function which is summable, nonnegative, and nonzero on a set of positive measure on $[-1,1]$. We study the problem of the least possible value
$$ i_n(h)=\inf\{\mu(p_n):p_n\in\mathscr P_n^0\} $$
of the measure $\mu(p_n)=\operatorname{mes}\{x\in[-1,1]:p_n(x)\ge0\}$ of the set of points of the interval at which the polynomial $p_n\in\mathscr P_n^0$ is nonnegative. We find the exact value of $i_n(h)$ under certain restrictions on the weight $h$. In particular, the Jacobi weight
$$ h^{(\alpha,\beta)}(x)=(1-x)^\alpha(1+x)^\beta $$
satisfies these restrictions provided that $-1<\alpha,\beta\le0$.

DOI: https://doi.org/10.4213/mzm1615

Full text: PDF file (215 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 1997, 62:3, 278–287

Bibliographic databases:

UDC: 517.518.86
Received: 15.11.1995
Revised: 10.11.1996

Citation: V. V. Arestov, V. Yu. Raevskaya, “An extremal problem for algebraic polynomials with zero mean value on an interval”, Mat. Zametki, 62:3 (1997), 332–342; Math. Notes, 62:3 (1997), 278–287

Citation in format AMSBIB
\Bibitem{AreRae97}
\by V.~V.~Arestov, V.~Yu.~Raevskaya
\paper An extremal problem for algebraic polynomials with zero mean value on an interval
\jour Mat. Zametki
\yr 1997
\vol 62
\issue 3
\pages 332--342
\mathnet{http://mi.mathnet.ru/mz1615}
\crossref{https://doi.org/10.4213/mzm1615}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1620046}
\zmath{https://zbmath.org/?q=an:0917.26012}
\elib{http://elibrary.ru/item.asp?id=13268376}
\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 3
\pages 278--287
\crossref{https://doi.org/10.1007/BF02360868}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000072500900002}


Linking options:
  • http://mi.mathnet.ru/eng/mz1615
  • https://doi.org/10.4213/mzm1615
  • http://mi.mathnet.ru/eng/mz/v62/i3/p332

    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. M. V. Deikalova, “About the sharp Jackson–Nikol'skii inequality for algebraic polynomials on a multidimensional Euclidean sphere”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S129–S142  mathnet  crossref  isi  elib
    2. K. S. Tikhanovtseva, “O naimenshei mere mnozhestva neotritsatelnosti algebraicheskogo mnogochlena s nulevym vzveshennym srednim znacheniem na otrezke”, Tr. IMM UrO RAN, 16, no. 4, 2010, 300–311  mathnet  elib
    3. S. V. Kuznetsov, K. S. Tikhanovtseva, “Mnozhestvo neotritsatelnosti naimenshei mery mnogochlenov s nulevym vzveshennym srednim znacheniem na otrezke”, Tr. IMM UrO RAN, 18, no. 4, 2012, 211–223  mathnet  elib
    4. K. S. Tikhanovtseva, “The rate of the smallest value of the weighted measure of the nonnegativity set for polynomials with zero mean value on a closed interval”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 195–201  mathnet  crossref  mathscinet  isi  elib
  • Математические заметки Mathematical Notes
    Number of views:
    This page:269
    Full text:116
    References:23
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020