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Matematicheskie Trudy, 2008, Volume 11, Number 1, Pages 192–207 (Mi mt123)  

This article is cited in 5 scientific papers (total in 5 papers)

Partially integral operators with bounded kernels

Yu. Kh. Eshkabilov

National University of Uzbekistan named after M. Ulugbek, Faculty of Mathematics and Mechanics
Full-text PDF (218 kB) Citations (5)
References:
Abstract: Let $\Omega=[a,b]^\nu$ and let $T$ be a partially integral operator defined in $ L_2(\Omega^2)$ as follows:
$$ (Tf)(x,y)=\int_\Omega q(x,s,y)f(s,y)\,d\mu(s). $$
In the article, we study the solvability of the partially integral Fredholm equations $f-\varkappa Tf=g$, where $g\in L_2(\Omega^2)$ is a given function and $\varkappa\in\mathbb C$. The notion of determinant (which is a measurable function on $\Omega$) is introduced for the operator $E-\varkappa T$, with $E$ is the identity operator in $L_2(\Omega^2)$. Some theorems on the spectrum of a bounded operator $T$ are proven.
Key words: partially integral operator, partially integral equation, integral Fredholm equation, Fredholm determinant, Fredholm minor, spectrum, limit spectrum, point spectrum.
Received: 18.04.2007
English version:
Siberian Advances in Mathematics, 2009, Volume 19, Issue 3, Pages 151–161
DOI: https://doi.org/10.3103/S1055134409030018
Bibliographic databases:
UDC: 517.984.53
Language: Russian
Citation: Yu. Kh. Eshkabilov, “Partially integral operators with bounded kernels”, Mat. Tr., 11:1 (2008), 192–207; Siberian Adv. Math., 19:3 (2009), 151–161
Citation in format AMSBIB
\Bibitem{Esh08}
\by Yu.~Kh.~Eshkabilov
\paper Partially integral operators with bounded kernels
\jour Mat. Tr.
\yr 2008
\vol 11
\issue 1
\pages 192--207
\mathnet{http://mi.mathnet.ru/mt123}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2437488}
\transl
\jour Siberian Adv. Math.
\yr 2009
\vol 19
\issue 3
\pages 151--161
\crossref{https://doi.org/10.3103/S1055134409030018}
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  • https://www.mathnet.ru/eng/mt/v11/i1/p192
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические труды Siberian Advances in Mathematics
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    Abstract page:455
    Full-text PDF :124
    References:71
    First page:1
     
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