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This article is cited in 12 scientific papers (total in 12 papers)
Convolution equation with a completely monotonic kernel on the half-line
N. B. Engibaryan, B. N. Enginbarian Byurakan Astrophysical Observatory, National Academy of Sciences of Armenia
Abstract:
The Wiener-Hopf integral equation
\begin {equation}
f(x)=g(x)+\int _0^\infty K(x-t) f(t)\,dt,\qquad
(I-K)f=g
\tag{{1}}\end {equation}
and the related problems of factorization are considered for the kernels
$\displaystyle K(\pm x)=\int _a^b e^{-xp}\,d\sigma _\pm (p)$, where
$\sigma _\pm (p)\uparrow{}$ and
$\displaystyle\mu \equiv \sum _\pm \int _a^b \frac 1p\,d\sigma _\pm (p)<+\infty$.
If $K$ is even or the symbol $1-\widehat K(s)$ has a positive zero, then the existence of Volterra factorization is proved in the supercritical case $\mu >1$. An extension of this result to the general supercritical case is indicated. The solubility of the corresponding equation (1) is proved for $g \in L_1(0,\infty )$. Several other results in the supercritical case or for
$\mu=1$ are obtained. The approach discussed is essentially based on the method of special factorization and on the generalized Ambartsumyan equations.
Received: 08.08.1995
Citation:
N. B. Engibaryan, B. N. Enginbarian, “Convolution equation with a completely monotonic kernel on the half-line”, Mat. Sb., 187:10 (1996), 53–72; Sb. Math., 187:10 (1996), 1465–1485
Linking options:
https://www.mathnet.ru/eng/sm164https://doi.org/10.1070/SM1996v187n10ABEH000164 https://www.mathnet.ru/eng/sm/v187/i10/p53
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Abstract page: | 510 | Russian version PDF: | 235 | English version PDF: | 11 | References: | 46 | First page: | 2 |
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