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Logarithms of moduli of entire functions are nowhere dense in the space of plurisubharmonic functions. (Russian, English) Zbl 1199.32010

Ukr. Mat. Zh. 60, No. 12, 1602-1609 (2008); translation in Ukr. Math. J. 60, No. 12, 1878-1888 (2008).
Summary: We prove that the set of logarithms of moduli of entire functions of several complex variables is nowhere dense in the space of plurisubharmonic functions equipped with a topology that is a generalization of the topology of uniform convergence on compact sets. This topology is generated by a metric in which plurisubharmonic functions form a complete metric space. Thus, the logarithms of moduli of entire functions form a set of the first Baire category.

MSC:

32A15 Entire functions of several complex variables
32U05 Plurisubharmonic functions and generalizations
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