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Mat. Sb., 2011, Volume 202, Number 10, Pages 87–98 (Mi msb7688)  

This article is cited in 12 scientific papers (total in 12 papers)

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

I. R. Kayumov

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University

Abstract: A necessary and sufficient condition for the series $\sum_{k=1}^\infty \frac{1}{t-z_k}$, $|z_k|<C |y_k|$, to converge in $L_p(\mathbb{R})$, $p>1$, is obtained.
Bibliography: 5 titles.

Keywords: simple partial fractions, Hardy's inequality, Fourier transform, Dirichlet series.

DOI: https://doi.org/10.4213/sm7688

Full text: PDF file (485 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2011, 202:10, 1493–1504

Bibliographic databases:

UDC: 517.538.52+517.444
MSC: Primary 41A20; Secondary 30B50
Received: 04.02.2010 and 08.04.2011

Citation: I. R. Kayumov, “Convergence of series of simple partial fractions in $L_p(\mathbb R)$”, Mat. Sb., 202:10 (2011), 87–98; Sb. Math., 202:10 (2011), 1493–1504

Citation in format AMSBIB
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    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, “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
    2. 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
    3. 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
    4. 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
    5. 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
    6. I. R. Kayumov, “On the Convergence of Series in Spaces of Integrable Functions”, Math. Notes, 95:6 (2014), 780–785  mathnet  crossref  crossref  mathscinet  isi  elib
    7. P. Chunaev, “Least deviation of logarithmic derivatives of algebraic polynomials from zero”, J. Approx. Theory, 185 (2014), 98–106  crossref  mathscinet  zmath  isi  elib  scopus
    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
    12. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
  • Математический сборник Sbornik: Mathematics (from 1967)
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