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Mat. Sb., 2002, Volume 193, Number 6, Pages 61–82 (Mi msb660)  

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

Conservative systems of integral convolution equations on the half-line and the entire line

N. B. Engibaryan

Byurakan Astrophysical Observatory, National Academy of Sciences of Armenia

Abstract: The following system of integral convolution equations is considered:
$$ f(x)=g(x)+\int_a^\infty K(x-t)f(t) dt, \qquad -\infty\leqslant a<\infty, $$
where the $(m\times m)$-matrix-valued function $K$ satisfies the conditions of conservativeness
$$ K_{ij}\in L_1(\mathbb R), \quad K_{ij}\geqslant 0, \qquad A\equiv\int_{-\infty}^\infty K(x) dx\in P_N, \qquad r(A)=1. $$
Here $P_N$ is the class of non-negative indecomposable $(m\times m)$-matrices and $r(A)$ is the spectral radius of the matrix $A$. For $a=0$ the equation in question is a conservative system of Wiener–Hopf integral equations. For $a=-\infty$ this is the multidimensional renewal equation on the entire line. Questions of the solubility of the inhomogeneous and the homogeneous equations, asymptotic and other properties of solutions are considered.
The method of non-linear factorization equations is applied and developed in combination with new results in multidimensional renewal theory.


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English version:
Sbornik: Mathematics, 2002, 193:6, 847–867

Bibliographic databases:

UDC: 517.9+519.24
MSC: 45B05, 45D05, 47G10
Received: 11.03.2001

Citation: N. B. Engibaryan, “Conservative systems of integral convolution equations on the half-line and the entire line”, Mat. Sb., 193:6 (2002), 61–82; Sb. Math., 193:6 (2002), 847–867

Citation in format AMSBIB
\by N.~B.~Engibaryan
\paper Conservative systems of integral convolution equations
on the~half-line and the~entire line
\jour Mat. Sb.
\yr 2002
\vol 193
\issue 6
\pages 61--82
\jour Sb. Math.
\yr 2002
\vol 193
\issue 6
\pages 847--867

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    This publication is cited in the following articles:
    1. Yengibarian N.B., “Factorization of Markov chains”, J. Theoret. Probab., 17:2 (2004), 459–481  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    2. N. B. Engibaryan, “On the fixed points of monotonic operators in the critical case”, Izv. Math., 70:5 (2006), 931–947  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. M. S. Sgibnev, “The matrix analogue of the Blackwell renewal theorem on the real line”, Sb. Math., 197:3 (2006), 369–386  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. M. S. Sgibnev, “On the existence of a solution of a homogeneous system of generalized Wiener–Hopf equations”, Izv. Math., 74:3 (2010), 595–606  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. N. B. Yengibaryan, A. G. Barseghyan, “Semiconservative Systems of Integral Equations with Two Kernels”, International Journal of Mathematics and Mathematical Sciences, 2011 (2011), 1  crossref  mathscinet  scopus  scopus  scopus
    6. Kh. A. Khachatryan, “On positive solutions of one class of nonlinear integral equations of Hammerstein–Nemytskiĭ type on the whole axis”, Trans. Moscow Math. Soc., 75 (2014), 1–12  mathnet  crossref  elib
    7. Kh. A. Khachatryan, T. G. Sardaryan, “O razreshimosti odnogo klassa nelineinykh integralnykh uravnenii tipa Urysona na vsei pryamoi”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 17:1 (2017), 40–50  mathnet  crossref  elib
    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. A. Kh. Khachatryan, Kh. A. Khachatryan, “Solvability of a nonlinear integral equation in dynamical string theory”, Theoret. and Math. Phys., 195:1 (2018), 529–537  mathnet  crossref  crossref  adsnasa  isi  elib
    10. Kh. A. Khachatryan, “O razreshimosti odnoi sistemy nelineinykh integralnykh uravnenii tipa Gammershteina na pryamoi”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 19:2 (2019), 164–181  mathnet  crossref  elib
    11. Kh. A. Khachatryan, H. S. Petrosyan, “On the Solvability of a Class of Nonlinear Hammerstein–Stieltjes Integral Equations on the Whole Line”, Proc. Steklov Inst. Math., 308 (2020), 238–249  mathnet  crossref  crossref  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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