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Izvestiya: Mathematics, 2009, Volume 73, Issue 5, Pages 921–937
DOI: https://doi.org/10.1070/IM2009v073n05ABEH002468
(Mi im2713)
 

This article is cited in 4 scientific papers (total in 4 papers)

On the factorization of integral operators on spaces of summable functions

N. B. Engibaryan

Institute of Mathematics, National Academy of Sciences of Armenia
References:
Abstract: We consider the factorization $I-K=(I-U^+)(I-U^-)$, where $I$ is the identity operator, $K$ is an integral operator acting on some Banach space of functions summable with respect to a measure $\mu$ on $(a,b)\subset(-\infty,+\infty)$ continuous relative to the Lebesgue measure,
\begin{equation*} (Kf)(x)=\int^b_ak(x,t)f(t)\mu(dt),\qquad x\in(a,b), \end{equation*}
and $U^\pm$ are the desired Volterra operators. A necessary and sufficient condition is found for the existence of this factorization for a rather wide class of operators $K$ with positive kernels and for Hilbert–Schmidt operators.
Keywords: functions summable with respect to a measure, integral operators, Volterra factorization.
Received: 02.08.2007
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2009, Volume 73, Issue 5, Pages 67–82
DOI: https://doi.org/10.4213/im2713
Bibliographic databases:
UDC: 517.9
Language: English
Original paper language: Russian
Citation: N. B. Engibaryan, “On the factorization of integral operators on spaces of summable functions”, Izv. RAN. Ser. Mat., 73:5 (2009), 67–82; Izv. Math., 73:5 (2009), 921–937
Citation in format AMSBIB
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\by N.~B.~Engibaryan
\paper On the factorization of integral operators on spaces of summable functions
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\yr 2009
\vol 73
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\pages 67--82
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\pages 921--937
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  • https://doi.org/10.1070/IM2009v073n05ABEH002468
  • https://www.mathnet.ru/eng/im/v73/i5/p67
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:663
    Russian version PDF:216
    English version PDF:19
    References:68
    First page:17
     
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