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This article is cited in 3 scientific papers (total in 3 papers)
Boundary properties of analytic solutions of differential equations of infinite order
Yu. F. Korobeinik
Abstract:
Let $\mathscr L(\lambda)$ be an entire function from the class $[1,0]$ with simple zeros $\{\lambda_n\}$ and let $\mathscr G$ be a bounded convex domain. In this paper particular solutions of the equation
\begin{equation}
(\mathscr L(D))(z)=f(z),\qquad z\in\mathscr G,
\tag{\text{I}}
\end{equation}
are constructed which are analytic in $\mathscr G$ and possess a definite smoothness on the boundary of $\mathscr G$, for the case in which $f$ is analytic in $\mathscr G$ and sufficiently smooth on the boundary. In particular, it is shown that if $\mathscr L(\lambda)$ is an entire function of completely regular growth with proximate order $\rho(r)$, $\rho(r)\to\rho$, $0<\rho<1$, with a positive indicator and a regular set of roots, then for an arbitrary function $f$, analytic in $\mathscr G$ and continuous on $\overline{\mathscr G}$, equation (I) has an effectively defined particular solution analytic in $\mathscr G$ and infinitely differentiable at each boundary point of $\mathscr G$.
Bibliography: 14 titles.
Received: 11.09.1980
Citation:
Yu. F. Korobeinik, “Boundary properties of analytic solutions of differential equations of infinite order”, Math. USSR-Sb., 43:3 (1982), 323–345
Linking options:
https://www.mathnet.ru/eng/sm2402https://doi.org/10.1070/SM1982v043n03ABEH002451 https://www.mathnet.ru/eng/sm/v157/i3/p364
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Abstract page: | 394 | Russian version PDF: | 120 | English version PDF: | 15 | References: | 85 |
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