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., 2010, Volume 201, Number 7, Pages 53–66 (Mi msb7596)  

This article is cited in 14 scientific papers (total in 14 papers)

Convergence of simple partial fractions in $L_p(\mathbb R)$

V. I. Danchenko

Vladimir State University

Abstract: The convergence in the $L_p(\mathbb R)$-metric of series whose partial sums are simple partial fractions is investigated. Several convergence conditions in terms of sequences of poles of these series are obtained.
Bibliography: 12 titles.

Keywords: simple partial fractions, duality, sparse sequences.

DOI: https://doi.org/10.4213/sm7596

Full text: PDF file (586 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2010, 201:7, 985–997

Bibliographic databases:

UDC: 517.538.52
MSC: Primary 41A25; Secondary 30B50
Received: 24.06.2009 and 05.04.2010

Citation: V. I. Danchenko, “Convergence of simple partial fractions in $L_p(\mathbb R)$”, Mat. Sb., 201:7 (2010), 53–66; Sb. Math., 201:7 (2010), 985–997

Citation in format AMSBIB
\Bibitem{Dan10}
\by V.~I.~Danchenko
\paper Convergence of simple partial fractions in~$L_p(\mathbb R)$
\jour Mat. Sb.
\yr 2010
\vol 201
\issue 7
\pages 53--66
\mathnet{http://mi.mathnet.ru/msb7596}
\crossref{https://doi.org/10.4213/sm7596}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2907814}
\zmath{https://zbmath.org/?q=an:1202.41012}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2010SbMat.201..985D}
\elib{http://elibrary.ru/item.asp?id=19066216}
\transl
\jour Sb. Math.
\yr 2010
\vol 201
\issue 7
\pages 985--997
\crossref{https://doi.org/10.1070/SM2010v201n07ABEH004099}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000281540900003}
\elib{http://elibrary.ru/item.asp?id=16974053}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77958589628}


Linking options:
  • http://mi.mathnet.ru/eng/msb7596
  • https://doi.org/10.4213/sm7596
  • http://mi.mathnet.ru/eng/msb/v201/i7/p53

    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. I. R. Kayumov, “Convergence of series of simple partial fractions in $L_p(\mathbb R)$”, Sb. Math., 202:10 (2011), 1493–1504  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. I. R. Kayumov, “Integral bounds for simple partial fractions”, Russian Math. (Iz. VUZ), 56:4 (2012), 27–37  mathnet  crossref  mathscinet
    3. I. R. Kayumov, “A Necessary Condition for the Convergence of Simple Partial Fractions in $L_p(\mathbb R)$”, Math. Notes, 92:1 (2012), 140–143  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. A. V. Kayumova, “Skhodimost ryadov prostykh drobei v $L_p(\mathbb R)$”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2012, 208–213  mathnet
    5. M. A. Komarov, “An example of nonuniqueness of a simple partial fraction of the best uniform approximation”, Russian Math. (Iz. VUZ), 57:9 (2013), 22–30  mathnet  crossref
    6. I. R. Kayumov, A. V. Kayumova, “Convergence of the imaginary parts of simplest fractions in $L_p(\mathbb R)$ for $p<1$”, J. Math. Sci. (N. Y.), 202:4 (2014), 553–559  mathnet  crossref
    7. V. I. Danchenko, A. E. Dodonov, “Estimates for $L_p$-norms of simple partial fractions”, Russian Math. (Iz. VUZ), 58:6 (2014), 6–15  mathnet  crossref
    8. M. A. Komarov, “A criterion for the best uniform approximation by simple partial fractions in terms of alternance”, Izv. Math., 79:3 (2015), 431–448  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. V. I. Danchenko, L. A. Semin, “Sharp quadrature formulas and inequalities between various metrics for rational functions”, Siberian Math. J., 57:2 (2016), 218–229  mathnet  crossref  crossref  mathscinet  isi  elib
    10. M. A. Komarov, “Approximation by linear fractional transformations of simple partial fractions and their differences”, Russian Math. (Iz. VUZ), 62:3 (2018), 23–33  mathnet  crossref  isi
    11. Chunaev P. Danchenko V., “Quadrature Formulas With Variable Nodes and Jackson-Nikolskii Inequalities For Rational Functions”, J. Approx. Theory, 228 (2018), 1–20  crossref  mathscinet  zmath  isi  scopus  scopus
    12. M. A. Komarov, “O priblizhenii spetsialnymi raznostyami naiprosteishikh drobei”, Algebra i analiz, 30:4 (2018), 47–60  mathnet
    13. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
    14. Komarov M.A., “Approximation to Constant Functions By Electrostatic Fields Due to Electrons and Positrons”, Lobachevskii J. Math., 40:1, SI (2019), 79–84  crossref  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:487
    Full text:111
    References:64
    First page:45

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