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

  • M. A. Girnyk

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.
Published
25.12.2008
How to Cite
Girnyk, M. A. “Logarithms of Moduli of Entire Functions Are Nowhere Dense in the Space of Plurisubharmonic Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, no. 12, Dec. 2008, pp. 1602 -, https://umj.imath.kiev.ua/index.php/umj/article/view/3274.
Section
Research articles