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.

UDC: 511.6+517.56

MSC: Primary 32A15; Secondary 32H99, 30A64, 30A70

Received: 05.03.1974

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

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