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Sbornik: Mathematics, 2009, Volume 200, Issue 8, Pages 1127–1148
DOI: https://doi.org/10.1070/SM2009v200n08ABEH004031
(Mi sm7466)
 

This article is cited in 16 scientific papers (total in 16 papers)

Approximation by simple partial fractions on the semi-axis

P. A. Borodin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: This paper investigates the simple partial fractions (that is, the logarithmic derivatives of polynomials) all of whose poles lie within the angular domain $\Lambda_\gamma=\{z:\arg z\in(\gamma,2\pi-\gamma)\}$, for any $\gamma\in[0,\pi/2]$. It is shown that they are contained in a proper half-space of the space $L_p({\mathbb R}_+)$ for any $p\in(1,p_0)$ (in particular, they are not dense in this space) and conversely, they are dense in $L_p({\mathbb R}_+)$ for any $p\geqslant p_0$, where $p_0=(2\pi-2\gamma)/(\pi-2\gamma)$. The distances from the poles of a simple partial fraction $r$ to the semi-axis ${\mathbb R}_+$ are estimated in terms of the degree of the fraction $r$ and its norm in $L_2({\mathbb R}_+)$. The approximation properties of sets of simple partial fractions of degree at most $n$ are investigated, as well as properties of the least deviations $\rho_n(f)$ from these sets for the functions $f\in L_2({\mathbb R}_+)$.
Bibliography: 14 titles.
Keywords: approximation, simple partial fraction, integral metrics.
Received: 24.10.2008 and 01.04.2009
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 8, Pages 25–44
DOI: https://doi.org/10.4213/sm7466
Bibliographic databases:
UDC: 517.538.5
MSC: 30E10, 41A20
Language: English
Original paper language: Russian
Citation: P. A. Borodin, “Approximation by simple partial fractions on the semi-axis”, Mat. Sb., 200:8 (2009), 25–44; Sb. Math., 200:8 (2009), 1127–1148
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2009v200n08ABEH004031
  • https://www.mathnet.ru/eng/sm/v200/i8/p25
  • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:1043
    Russian version PDF:249
    English version PDF:12
    References:70
    First page:31
     
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