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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
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
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
Linking options:
https://www.mathnet.ru/eng/mt123 https://www.mathnet.ru/eng/mt/v11/i1/p192
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Abstract page: | 455 | Full-text PDF : | 124 | References: | 71 | First page: | 1 |
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