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An addition to the $\cos\pi\rho$-theorem for subharmonic and entire functions of zero lower order

Author: I. E. Chyzhykov
Journal: Proc. Amer. Math. Soc. 130 (2002), 517-528
MSC (2000): Primary 30D15, 31A05
Published electronically: June 21, 2001
MathSciNet review: 1862132
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We obtain a sharp asymptotic relation between the infimum and the maximum on a circle of a subharmonic function of zero lower order. An example is constructed, which shows the sharpness of the relation in the class of entire functions of zero order such that $\log M(r,f)/\log ^2 r\to+\infty$, where $M(r,f)=\max \{\vert f(z)\vert: \vert z\vert=r\}$ as $r\to+\infty$.

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Additional Information

I. E. Chyzhykov
Affiliation: Department of Mechanics and Mathematics, Lviv National University, Universytetska 1, Lviv, 79000, Ukraine

Keywords: Subharmonic function, $\cos\pi\rho$-theorem, entire function, minimum modulus
Received by editor(s): July 5, 2000
Published electronically: June 21, 2001
Additional Notes: The author was supported in part by INTAS, Grant # 99-00089
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2001 American Mathematical Society

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