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 Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 1, Pages 65–95 (Mi izv1765)

Growth of entire functions of two complex variables that are slowly increasing in one of the variables

V. P. Petrenko

Abstract: This article studies the asymptotic properties of one general class of entire functions of two complex variables. The class consists of those functions which from the point of view of growth and value distribution theory are the natural generalization of $p$-dimensional entire curves. For functions in this class the concepts of defect and deviation are defined, sharp bounds for these quantities are deduced, and it is shown that the set of all positive deviations is an exceptional set. Corresponding quantities are introduced and some of their properties are described for functions of $n$ ($n>2$) complex variables.
Bibliography: 26 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:1, 63–92

Bibliographic databases:

UDC: 511.6+517.56
MSC: Primary 32A15; Secondary 32H99, 30A64, 30A70

Citation: V. P. Petrenko, “Growth of entire functions of two complex variables that are slowly increasing in one of the variables”, Izv. Akad. Nauk SSSR Ser. Mat., 40:1 (1976), 65–95; Math. USSR-Izv., 10:1 (1976), 63–92

Citation in format AMSBIB
\Bibitem{Pet76} \by V.~P.~Petrenko \paper Growth of entire functions of two complex variables that are slowly increasing in one of the variables \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1976 \vol 40 \issue 1 \pages 65--95 \mathnet{http://mi.mathnet.ru/izv1765} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=414916} \zmath{https://zbmath.org/?q=an:0326.32005} \transl \jour Math. USSR-Izv. \yr 1976 \vol 10 \issue 1 \pages 63--92 \crossref{https://doi.org/10.1070/IM1976v010n01ABEH001679}