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Matematicheskie Zametki, 1975, Volume 18, Issue 3, Pages 445–452 (Mi mzm7673)  

The lower order of functions of the class B

S. Yu. Favorov

Kharkov State University
Abstract: The class of functions Φ(z,t) defined for zCn and t0 such that the functions Φ(z,|w|), wC, are plurisubharmonic in Cn+1 is called the class B. A typical example of functions of the class B are functions of the form lnMg(z,t)=lnsup|w|=t|g(z,w)| where g(z,w), zCn, wC, is an entire function in Cn+1.
In this note it is proved under certain restrictions on the function Φ(z,t)B that its lower order relative to the variable t is the same for all zCn except, possibly, for the points z of a set of zero Γ capacity.
Received: 25.02.1974
English version:
Mathematical Notes, 1975, Volume 18, Issue 3, Pages 853–857
DOI: https://doi.org/10.1007/BF01095445
Bibliographic databases:
UDC: 519.55
Language: Russian
Citation: S. Yu. Favorov, “The lower order of functions of the class B”, Mat. Zametki, 18:3 (1975), 445–452; Math. Notes, 18:3 (1975), 853–857
Citation in format AMSBIB
\Bibitem{Fav75}
\by S.~Yu.~Favorov
\paper The lower order of functions of the class $\mathfrak B$
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 3
\pages 445--452
\mathnet{http://mi.mathnet.ru/mzm7673}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=393573}
\zmath{https://zbmath.org/?q=an:0321.32003}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 3
\pages 853--857
\crossref{https://doi.org/10.1007/BF01095445}
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