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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Abstract:

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
Email: matstud@franko.lviv.ua

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06188-3
PII: S 0002-9939(01)06188-3
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