On Subharmonic Functions of the First Order with Restrictions on the Real Axis
Ключові слова:
proximate order, functions of the class A, functions of completely regular growthАнотація
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.
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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.
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