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This article is cited in 9 scientific papers (total in 9 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 $\mu=1$.
Received: 30.01.1995
Citation:
N. B. Engibaryan, “Convolution equations containing singular probability distributions”, Izv. Math., 60:2 (1996), 251–279
Linking options:
https://www.mathnet.ru/eng/im70https://doi.org/10.1070/IM1996v060n02ABEH000070 https://www.mathnet.ru/eng/im/v60/i2/p21
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Abstract page: | 617 | Russian version PDF: | 253 | English version PDF: | 23 | References: | 84 | First page: | 4 |
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