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 Mat. Sb. (N.S.), 1981, Volume 115(157), Number 3(7), Pages 364–390 (Mi msb2402)

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
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.

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English version:
Mathematics of the USSR-Sbornik, 1982, 43:3, 323–345

Bibliographic databases:

UDC: 517.9
MSC: Primary 34A35, 34B05; Secondary 30D15

Citation: Yu. F. Korobeinik, “Boundary properties of analytic solutions of differential equations of infinite order”, Mat. Sb. (N.S.), 115(157):3(7) (1981), 364–390; Math. USSR-Sb., 43:3 (1982), 323–345

Citation in format AMSBIB
\Bibitem{Kor81} \by Yu.~F.~Korobeinik \paper Boundary properties of analytic solutions of differential equations of infinite order \jour Mat. Sb. (N.S.) \yr 1981 \vol 115(157) \issue 3(7) \pages 364--390 \mathnet{http://mi.mathnet.ru/msb2402} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=628216} \zmath{https://zbmath.org/?q=an:0492.34010|0475.34007} \transl \jour Math. USSR-Sb. \yr 1982 \vol 43 \issue 3 \pages 323--345 \crossref{https://doi.org/10.1070/SM1982v043n03ABEH002451} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. B. Sherstyukov, “Representation of the reciprocal of an entire function by series of partial fractions and exponential approximation”, Sb. Math., 200:3 (2009), 455–469
2. V. B. Sherstyukov, “Expanding the reciprocal of an entire function with zeros in a strip in a Kreǐn series”, Sb. Math., 202:12 (2011), 1853–1871
3. V. B. Sherstyukov, “Asimptoticheskie svoistva tselykh funktsii s zadannym zakonom raspredeleniya kornei”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 104–129
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