A Property of Azarin's Limit Set of Subharmonic Functions

Анотація

Let $v(z)$ be a subharmonic function of order $\rho>0$, and $\mathrm{Fr}(v)$ be the limit set in the sense of Azarin. Let $z$ be fixed and $I(z)=\{u(z):u\in \mathrm{Fr}(v)\}$. We prove that $I(z)$ is either a closed interval or a semiclosed interval which does not contain its infimum.

Mathematics Subject Classification: 31A05.