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 Mat. Zametki, 1976, Volume 19, Issue 6, Pages 899–911 (Mi mz7812)

Estimates of $n$-diameters of some classes of functions analytic on Riemann surfaces

V. P. Zakharyuta, N. I. Skiba

Rostov State University

Abstract: This study concerns the class $A_K^D$ of functions $x$ analytic in a domain $D$ of an open Riemann surface and satisfying there the inequality $|x|<1$ with metric defined by the norm of the space $C(K)$ of functions continuous on the compact subset $K\subset D$. The asymptotic formula
$$\lim_{n\to\infty}[d_n(A_K^D)]^{1/n}=e^{-1/\tau},$$
is established, where $D$ is a finitely connected domain of Carathéodory type, $K\subset D$ is a regular compact subset such thatdsetmnk is connected, and $\tau=\tau(D,K)$ is the flux of harmonic measure of the set $\partial D$ relative to the $D\setminus K$ through any rectifiable contour separating $\partial D$ and $K$.

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English version:
Mathematical Notes, 1976, 19:6, 525–532

Bibliographic databases:

UDC: 517.5

Citation: V. P. Zakharyuta, N. I. Skiba, “Estimates of $n$-diameters of some classes of functions analytic on Riemann surfaces”, Mat. Zametki, 19:6 (1976), 899–911; Math. Notes, 19:6 (1976), 525–532

Citation in format AMSBIB
\Bibitem{ZakSki76} \by V.~P.~Zakharyuta, N.~I.~Skiba \paper Estimates of $n$-diameters of some classes of functions analytic on Riemann surfaces \jour Mat. Zametki \yr 1976 \vol 19 \issue 6 \pages 899--911 \mathnet{http://mi.mathnet.ru/mz7812} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=419783} \zmath{https://zbmath.org/?q=an:0375.46028} \transl \jour Math. Notes \yr 1976 \vol 19 \issue 6 \pages 525--532 \crossref{https://doi.org/10.1007/BF01149932} 

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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. O. G. Parfenov, “Asymptotics of singular numbers of imbedding operators for certain classes of analytic functions”, Math. USSR-Sb., 43:4 (1982), 563–571
2. O. G. Parfenov, “Asymptotic behavior of the diameters of certain classes of analytic functions”, Funct. Anal. Appl., 15:4 (1981), 304–305
3. O. G. Parfenov, “Widths of a class of analytic functions”, Math. USSR-Sb., 45:2 (1983), 283–289
4. O. G. Parfenov, “Estimates of the singular numbers of the Carleson imbedding operator”, Math. USSR-Sb., 59:2 (1988), 497–514
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