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 Mat. Sb. (N.S.), 1976, Volume 100(142), Number 4(8), Pages 507–533 (Mi msb3005)

Some boundary properties of abstract analytic functions, and their applications

A. A. Danilevich

Abstract: We study boundary properties of analytic functions of the Hardy and Nevanlinna classes, defined in the unit disk, with values in a Fréchet space $E'$, the strong dual of a locally convex topological space $E$. In particular, necessary and sufficient conditions are given for angular limiting values of these functions to exist almost everywhere on a subset $M$, $\operatorname{mes}M>0$, of the unit circle in the topology of the space $E'$. The results obtained are used to investigate boundary properties of compact families of complex-valued holomorphic functions.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1976, 29:4, 453–474

Bibliographic databases:

UDC: 513.881+517.53
MSC: Primary 30A96; Secondary 30A72, 30A78, 32A10, 46J15

Citation: A. A. Danilevich, “Some boundary properties of abstract analytic functions, and their applications”, Mat. Sb. (N.S.), 100(142):4(8) (1976), 507–533; Math. USSR-Sb., 29:4 (1976), 453–474

Citation in format AMSBIB
\Bibitem{Dan76} \by A.~A.~Danilevich \paper Some boundary properties of abstract analytic functions, and their applications \jour Mat. Sb. (N.S.) \yr 1976 \vol 100(142) \issue 4(8) \pages 507--533 \mathnet{http://mi.mathnet.ru/msb3005} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=419782} \zmath{https://zbmath.org/?q=an:0332.30018} \transl \jour Math. USSR-Sb. \yr 1976 \vol 29 \issue 4 \pages 453--474 \crossref{https://doi.org/10.1070/SM1976v029n04ABEH003681} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976FB65000003} 

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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. Nawrocki M., “The Frechet Envelopes of Vector-Valued Smirnov Classes”, Studia Math., 94:2 (1989), 163–177
2. Wolfgang Hensgen, “On the dual space of Hp(X), 1 < p < ∞”, Journal of Functional Analysis, 92:2 (1990), 348
3. Bu S., “On the Analytic Radon-Nikodym Property for Bounded Subsets in Banach-Spaces”, J. Lond. Math. Soc.-Second Ser., 47:Part 3 (1993), 484–496
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