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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2012, Volume 154, Book 1, Pages 208–213 (Mi uzku1112)  

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

The convergence of series of simple fractions in $L_p(\mathbb R)$.

A. V. Kayumova

Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University

Abstract: The convergence of series of simple fractions in $L_p(\mathbb R)$ has been investigated. In particular, necessary and sufficient conditions for the convergence of series with coefficients $\frac{p_k}{t-z_k}$, where $p_k$ is a sequence of positive numbers, in $L_p(\mathbb R)$ have been obtained.

Keywords: simple fractions, Hardy's inequality.

Full text: PDF file (177 kB)
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UDC: 517.538.52+517.444
Received: 16.01.2012

Citation: A. V. Kayumova, “The convergence of series of simple fractions in $L_p(\mathbb R)$.”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 154, no. 1, Kazan University, Kazan, 2012, 208–213

Citation in format AMSBIB
\Bibitem{Kay12}
\by A.~V.~Kayumova
\paper The convergence of series of simple fractions in $L_p(\mathbb R)$.
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2012
\vol 154
\issue 1
\pages 208--213
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1112}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
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