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Mathematics of the USSR-Izvestiya, 1970, Volume 4, Issue 6, Pages 1273–1354
DOI: https://doi.org/10.1070/IM1970v004n06ABEH000956
(Mi im2470)
 

This article is cited in 4 scientific papers (total in 5 papers)

Boundary properties of subclasses of meromorphic functions of bounded form

M. M. Dzhrbashyan, V. S. Zakharyan
References:
Abstract: One of the authors [1] has constructed a complete factorization theory for classes of functions meromorphic in the disk $|z|<1$. Such a class $N\{\omega\}$ is associated with a given positive continuous function $\omega(x)$ on $[0,1)$ satisfying the conditions $\omega(0)=1$ and $\omega(x)\in L[0,1)$, contains an arbitrary function meromorphic in $|z|<1$ for a suitable choice of $\omega(x)$, and coincides in the special case $\omega(x)\equiv1$ with the class $N$ of functions of bounded form of R. Nevanlinna ([2], Chapter VI).
In this present paper we study boundary properties of the classes $N\{\omega\}$, which are contained in $N$ when $\omega(x)\uparrow+\infty$ as $x\uparrow1$.
We will prove a number of theorems giving various refined metric characteristics of those exceptional sets $E\subset[0{,}2\pi]$ of measure zero on which a function in the class $N\{\omega\}\subset N$ may not possess a radial boundary value.
A characteristic of the exceptional sets $E$ will be given in terms of the convex capacity $\operatorname{Cap}\{E;\lambda_n\}$ with respect to a sequence$\{\lambda_n\}$, the Hausdorff $h$-measure $m(E;h)$, or the measure $C_\omega(E)$ associated with the function $\omega(x)$ generating the given class $N\{\omega\}\subset N$.
Received: 29.05.1970
Bibliographic databases:
UDC: 517.5
MSC: Primary 30A72; Secondary 30A44, 30A68, 30A70, 30A76
Language: English
Original paper language: Russian
Citation: M. M. Dzhrbashyan, V. S. Zakharyan, “Boundary properties of subclasses of meromorphic functions of bounded form”, Math. USSR-Izv., 4:6 (1970), 1273–1354
Citation in format AMSBIB
\Bibitem{DzhZak70}
\by M.~M.~Dzhrbashyan, V.~S.~Zakharyan
\paper Boundary properties of subclasses of meromorphic functions of
bounded form
\jour Math. USSR-Izv.
\yr 1970
\vol 4
\issue 6
\pages 1273--1354
\mathnet{http://mi.mathnet.ru//eng/im2470}
\crossref{https://doi.org/10.1070/IM1970v004n06ABEH000956}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=310250}
\zmath{https://zbmath.org/?q=an:0207.37305}
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  • https://doi.org/10.1070/IM1970v004n06ABEH000956
  • https://www.mathnet.ru/eng/im/v34/i6/p1262
    Remarks
    This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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