2019
Том 71
№ 11

All Issues

Girnyk M. A.

Articles: 4
Article (Russian)

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

Girnyk M. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 12. - pp. 1602 – 1609

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.

Brief Communications (Russian)

Approximation of functions subharmonic in a disk by the logarithm of the modulus of an analytic function

Girnyk M. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1080–1083

Yulmukhametov's result concerning the approximation of a function subharmonic in a bounded domain by the logarithm of the modulus of an analytic function is supplemented with an estimate of the exceptional set in the important case of a disk. We show that this approximation is unimprovable in a certain sense.

Article (Ukrainian)

Defects of derivatives of an entire function

Girnyk M. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1981. - 33, № 4. - pp. 510–513

Article (Ukrainian)

On the inverse problem in va Lue distribution theory for functions analytic in the unit disk

Girnyk M. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1977. - 29, № 1. - pp. 32–39