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Izv. RAN. Ser. Mat., 1996, Volume 60, Issue 2, Pages 21–48 (Mi izv70)  

This article is cited in 5 scientific papers (total in 5 papers)

Convolution equations containing singular probability distributions

N. B. Engibaryan


Abstract: The article is devoted to equations of the form
\begin{equation} \varphi(x)=g(x)-\int_0^\infty\varphi(t) dT(x-t), \tag{1} \end{equation}
where $T$ is a continuous function of bounded variation on $(-\infty;\infty)$ containing a singular component. First we study asymptotic and other properties of the solutions of formal Volterra equations (1) corresponding to $T(x)=0$ for $x\leqslant 0$. Next we introduce and study non-linear factorization equations (NFE) for (1). Factorization is constructed in the case when $T(-\infty)=0$, $T(x)\uparrow$ in $x$, and $T(+\infty)=\mu\leqslant 1$. With the aid of this factorization, we prove existence theorems for homogeneous $(g=0)$ and non-homogeneous equations in the singular case $\mu=1$.

DOI: https://doi.org/10.4213/im70

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English version:
Izvestiya: Mathematics, 1996, 60:2, 249–280

Bibliographic databases:

UDC: 517.9
MSC: 45E10
Received: 30.01.1995

Citation: N. B. Engibaryan, “Convolution equations containing singular probability distributions”, Izv. RAN. Ser. Mat., 60:2 (1996), 21–48; Izv. Math., 60:2 (1996), 249–280

Citation in format AMSBIB
\Bibitem{Eng96}
\by N.~B.~Engibaryan
\paper Convolution equations containing singular probability distributions
\jour Izv. RAN. Ser. Mat.
\yr 1996
\vol 60
\issue 2
\pages 21--48
\mathnet{http://mi.mathnet.ru/izv70}
\crossref{https://doi.org/10.4213/im70}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1399417}
\zmath{https://zbmath.org/?q=an:0882.45002}
\transl
\jour Izv. Math.
\yr 1996
\vol 60
\issue 2
\pages 249--280
\crossref{https://doi.org/10.1070/IM1996v060n02ABEH000070}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0043046959}


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  • https://doi.org/10.4213/im70
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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. N. B. Engibaryan, “Renewal equations on the semi-axis”, Izv. Math., 63:1 (1999), 57–71  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Yengibarian N.B., “Renewal equation on the whole line”, Stochastic Processes and Their Applications, 85:2 (2000), 237–247  crossref  mathscinet  zmath  isi  scopus  scopus
    3. 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
    4. M. S. Sgibnev, “Homogeneous conservative Wiener–Hopf equation”, Sb. Math., 198:9 (2007), 1341–1350  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Kh. A. Khachatryan, “O razreshimosti odnoi nachalno-kraevoi zadachi dlya nelineinogo integro-differentsialnogo uravneniya s nekompaktnym operatorom tipa Gammershteina”, Tr. IMM UrO RAN, 19, no. 3, 2013, 308–315  mathnet  mathscinet  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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