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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
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
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
Linking options:
https://www.mathnet.ru/eng/im2713https://doi.org/10.1070/IM2009v073n05ABEH002468 https://www.mathnet.ru/eng/im/v73/i5/p67
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Abstract page: | 663 | Russian version PDF: | 216 | English version PDF: | 19 | References: | 68 | First page: | 17 |
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