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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 z∈Cn and t⩾0 such that the functions Φ(z,|w|), w∈C, 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), z∈Cn, w∈C, 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 z∈Cn except, possibly, for the points z of a set of zero Γ capacity.
Received: 25.02.1974
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
Linking options:
https://www.mathnet.ru/eng/mzm7673 https://www.mathnet.ru/eng/mzm/v18/i3/p445
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Abstract page: | 273 | Full-text PDF : | 86 | First page: | 1 |
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