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Mat. Sb., 1996, Volume 187, Number 10, Pages 53–72 (Mi msb164)  

This article is cited in 11 scientific papers (total in 11 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.

DOI: https://doi.org/10.4213/sm164

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English version:
Sbornik: Mathematics, 1996, 187:10, 1465–1485

Bibliographic databases:

UDC: 517.968
MSC: 45E10, 47G10
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

Citation in format AMSBIB
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\by N.~B.~Engibaryan, B.~N.~Enginbarian
\paper Convolution equation with a~completely monotonic kernel on the~half-line
\jour Mat. Sb.
\yr 1996
\vol 187
\issue 10
\pages 53--72
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\transl
\jour Sb. Math.
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\vol 187
\issue 10
\pages 1465--1485
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    This publication is cited in the following articles:
    1. Kh. A. Khachatryan, “Application of the albedo shifting method to an integral equation”, Comput. Math. Math. Phys., 42:6 (2002), 870–877  mathnet  mathscinet  zmath
    2. L. G. Arabadzhyan, “The Wiener–Hopf Integral Equation in the Supercritical Case”, Math. Notes, 76:1 (2004), 10–17  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. S. M. Andriyan, A. Kh. Khachatryan, “On one problem in physical kinetics”, Comput. Math. Math. Phys., 45:11 (2005), 1982–1989  mathnet  mathscinet  zmath
    4. B. N. Enginbarian, “On the Convolution Equation with Positive Kernel Expressed via an Alternating Measure”, Math. Notes, 81:5 (2007), 620–627  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. N. B. Engibaryan, A. Kh. Khachatryan, “Integro-differential equation of non-local wave interaction”, Sb. Math., 198:6 (2007), 839–855  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Khachatryan K.A., “One-parameter family of solutions for one class of hammerstein nonlinear equations on a half-line”, Dokl. Math., 80:3 (2009), 872–876  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    7. Kh. A. Khachatryan, “On solvability of some classes of Urysohn nonlinear integral equations with noncompact operators”, Ufimsk. matem. zhurn., 2:2 (2010), 102–117  mathnet  zmath
    8. A. Kh. Khachatryan, Kh. A. Khachatryan, “On solvability of one class of Hammerstein nonlinear integral equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2010, no. 2, 67–83  mathnet  mathscinet  zmath
    9. N. B. Engibaryan, A. Kh. Khachatryan, “Solvability of an integrodifferential equation arising in the nonlocal interaction of waves”, Comput. Math. Math. Phys., 54:5 (2014), 834–844  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    10. G. A. Grigoryan, “On a Criterion for the Invertibility of Integral Operators of the Second Kind in the Space of Summable Functions on the Semiaxis”, Math. Notes, 96:6 (2014), 914–920  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. Arabajyan L.G., “A Wiener-Hopf Integral Equation With a Nonsymmetric Kernel in the Supercritical Case”, J. Contemp. Math. Anal.-Armen. Aca., 54:5 (2019), 253–262  crossref  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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