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

This article is cited in 9 scientific papers (total in 9 papers)

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

N. B. Engibaryan, L. G. Arabadzhyan


Abstract: Systems of Wiener–Hopf integral equations
\begin{equation} f(x)=g(x)+\int_0^\infty T(x-t)f(t) dt \end{equation}
and corresponding nonlinear factorization equations
\begin{align} U(x)&=T(x)+\int_0^\infty V(t)U(x+t) dt, \nonumber
V(x)&=T(-x)+\int_0^\infty V(x+t)U(t) dt,\qquad x>0, \end{align}
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
Received: 19.04.1982

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
    Related articles on Google Scholar: Russian articles, English articles

    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  mathnet  mathscinet  zmath  isi
    2. N. B. Engibaryan, “Renewal theorems for a system of integral equations”, Sb. Math., 189:12 (1998), 1795–1808  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Elias Wegert, Lothar von Wolfersdorf, “A solution method for the linear Chandrasekhar equation”, Math Meth Appl Sci, 29:15 (2006), 1767  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  mathscinet  zmath  isi  elib
    7. Khachatryan Kh.A., “On Some Systems of Nonlinear Integral Hammerstein-Type Equations on the Semiaxis”, Ukr. Math. J., 62:4 (2010), 630–647  crossref  mathscinet  zmath  isi
    8. N. B. Engibaryan, “On the factorization of matrix and operator Wiener–Hopf integral equations”, Izv. Math., 82:2 (2018), 273–282  mathnet  crossref  crossref  adsnasa  isi  elib
    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  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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