2017
Том 69
№ 9

All Issues

Logarithms of moduli of entire functions are nowhere dense in the space of plurisubharmonic functions

Girnyk M. A.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 12, pp 1878-1888.

Citation Example: Girnyk M. A. Logarithms of moduli of entire functions are nowhere dense in the space of plurisubharmonic functions // Ukr. Mat. Zh. - 2008. - 60, № 12. - pp. 1602 – 1609.

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