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 Mat. Sb. (N.S.), 1984, Volume 124(166), Number 2(6), Pages 189–216 (Mi msb2047)

Systems of Wiener–Hopf integral equations, and nonlinear factorization equations

N. B. Engibaryan, L. G. Arabadzhyan

Abstract: Systems of Wiener–Hopf integral equations
$$f(x)=g(x)+\int_0^\infty T(x-t)f(t) dt$$
and corresponding nonlinear factorization equations
\begin{align} U(x)&=T(x)+\int_0^\infty V(t)U(x+t) dt, \nonumber
are studied. It is assumed that $T$ is a matrix-valued function with nonnegative components from $L_1(-\infty,\infty)$, with $\mu=r(A)\leqslant1$, where $\displaystyle A=\int_{-\infty}^\infty T(x) dx$, and $r(A)$ is the spectral radius of the matrix $A$.
The conservative case $\mu=1$, to which major attention is given, falls outside the general theory of Wiener–Hopf integral equations, since the symbol of equation (1) degenerates.
A number of results have been obtained about the properties of the solution of the factorization equation (2), and about the existence, asymptotics and other properties of the solution of the homogeneous and nonhomogeneous conservative equation (1).
Bibliography: 21 titles.

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English version:
Mathematics of the USSR-Sbornik, 1985, 52:1, 181–208

Bibliographic databases:

UDC: 517.9
MSC: 45F15, 45E10

Citation: N. B. Engibaryan, L. G. Arabadzhyan, “Systems of Wiener–Hopf integral equations, and nonlinear factorization equations”, Mat. Sb. (N.S.), 124(166):2(6) (1984), 189–216; Math. USSR-Sb., 52:1 (1985), 181–208

Citation in format AMSBIB
\Bibitem{EngAra84} \by N.~B.~Engibaryan, L.~G.~Arabadzhyan \paper Systems of Wiener--Hopf integral equations, and nonlinear factorization equations \jour Mat. Sb. (N.S.) \yr 1984 \vol 124(166) \issue 2(6) \pages 189--216 \mathnet{http://mi.mathnet.ru/msb2047} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=746067} \zmath{https://zbmath.org/?q=an:0582.45017|0566.45007} \transl \jour Math. USSR-Sb. \yr 1985 \vol 52 \issue 1 \pages 181--208 \crossref{https://doi.org/10.1070/SM1985v052n01ABEH002884} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Engibaryan N. Arabadzhyan L., “Some Factorization Problems for Convolution Integral-Operators”, Differ. Equ., 26:8 (1990), 1069–1078
2. N. B. Engibaryan, “Renewal theorems for a system of integral equations”, Sb. Math., 189:12 (1998), 1795–1808
3. N. B. Engibaryan, “Conservative systems of integral convolution equations on the half-line and the entire line”, Sb. Math., 193:6 (2002), 847–867
4. Elias Wegert, Lothar von Wolfersdorf, “A solution method for the linear Chandrasekhar equation”, Math Meth Appl Sci, 29:15 (2006), 1767
5. Khachatryan, KA, “Solvability of Vector Integro-Differential Equations of Convolution Type on the Semiaxis”, Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences, 43:5 (2008), 305
6. Ts. È. Terdzhyan, A. Kh. Khachatryan, “About one system of integral equations in kinetic theory”, Comput. Math. Math. Phys., 49:4 (2009), 691–697
7. Khachatryan Kh.A., “On Some Systems of Nonlinear Integral Hammerstein-Type Equations on the Semiaxis”, Ukr. Math. J., 62:4 (2010), 630–647
8. N. B. Engibaryan, “On the factorization of matrix and operator Wiener–Hopf integral equations”, Izv. Math., 82:2 (2018), 273–282
9. Khachatryan Kh.A. Terdzhyan Ts.E. Sardanyan T.G., “On the Solvability of One System of Nonlinear Hammerstein-Type Integral Equations on the Semiaxis”, Ukr. Math. J., 69:8 (2018), 1287–1305
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