On Subharmonic Functions of the First Order with Restrictions on the Real Axis

Автор(и)

  • I. V. Poedintseva Department of Mechanics and Mathematics, V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61077, Ukraine

Ключові слова:

proximate order, functions of the class A, functions of completely regular growth

Анотація

Subharmonic functions $v$ of the first proximate order $\rho(r)$ with the integral $\displaystyle\int_0^R \frac{t^{1-\rho(t)}(v(t)+v(-t))}{1+t^2}dt$ bounded with respect to $R$ are studied. This is an extension of a result by N.I. Akhiezer, who studied the case $\rho(r)\equiv 1$, $v(z)=\ln |f(z)|$, where $f(z)$ is an entire function.

Mathematics Subject Classification: 31A05.

Downloads

Як цитувати

(1)
Poedintseva, I. V. On Subharmonic Functions of the First Order with Restrictions on the Real Axis. Журн. мат. фіз. анал. геом. 2008, 4, 380-394.

Номер

Розділ

Статті

Завантаження

Дані завантаження ще не доступні.