RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find






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


Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 1, Pages 66–78 (Mi timm205)  

This article is cited in 3 scientific papers (total in 3 papers)

Pointwise estimates of polynomials orthogonal on a circle with respect to a weight not belonging to the spaces $L^r$ ($r>1$).

V. M. Badkov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Two-sided pointwise estimates are established for polynomials that are orthogonal on the circle $|z|=1$ with the weight $\varphi(\tau):=h(\tau)|\sin(\tau/2)|^{-1}g(|\sin(\tau/2)|)$ ($\tau\in\mathbb R$), where $g(t)$ is a concave modulus of continuity slowly changing at zero such that $t^{-1}g(t)\in L^1[0,1]$ and $h(\tau)$ is a positive function from the class $C_{2\pi}$ with a modulus of continuity satisfying the integral Dini condition. The obtained estimates are applied to find the order of the distance from the point $t=1$ to the greatest zero of a polynomial orthogonal on the segment [-1,1].

Keywords: orthogonal polynomials, pointwise estimates, the Szegő function

Full text: PDF file (205 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 265, suppl. 1, S64–S77

Bibliographic databases:

UDC: 517.5
Received: 20.02.2009

Citation: V. M. Badkov, “Pointwise estimates of polynomials orthogonal on a circle with respect to a weight not belonging to the spaces $L^r$ ($r>1$).”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 1, 2009, 66–78; Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S64–S77

Citation in format AMSBIB
\Bibitem{Bad09}
\by V.~M.~Badkov
\paper Pointwise estimates of polynomials orthogonal on a~circle with respect to a~weight not belonging to the spaces $L^r$ ($r>1$).
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 1
\pages 66--78
\mathnet{http://mi.mathnet.ru/timm205}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2728956}
\elib{http://elibrary.ru/item.asp?id=11929778}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 265
\issue , suppl. 1
\pages S64--S77
\crossref{https://doi.org/10.1134/S0081543809060066}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000268192700006}


Linking options:
  • http://mi.mathnet.ru/eng/timm205
  • http://mi.mathnet.ru/eng/timm/v15/i1/p66

    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. V. M. Badkov, “Some properties of Jacobi polynomials orthogonal on a circle”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S49–S58  mathnet  crossref  isi  elib
    2. V. M. Badkov, “Estimates of the Lebesgue function of Fourier sums over trigonometric polynomials orthogonal with a weight not belonging to the spaces $L^r$ $(r>1)$”, Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 21–32  mathnet  crossref  isi  elib
    3. Vasil'eva A.A., “Kolmogorov widths of weighted Sobolev classes on a domain for a special class of weights”, Russ. J. Math. Phys., 18:3 (2011), 353–385  crossref  mathscinet  zmath  adsnasa  isi  scopus
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Number of views:
    This page:189
    Full text:52
    References:42
    First page:3

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