Proceedings of the American Mathematical Society

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

Author(s): I. E. Chyzhykov
Journal: Proc. Amer. Math. Soc. 130 (2002), 517-528.
MSC (2000): Primary 30D15, 31A05
Posted: June 21, 2001
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30D15, 31A05

I. E. Chyzhykov
Affiliation: Department of Mechanics and Mathematics, Lviv National University, Universytetska 1, Lviv, 79000, Ukraine
Email: matstud@franko.lviv.ua

DOI: 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
Posted: June 21, 2001
Additional Notes: The author was supported in part by INTAS, Grant # 99-00089
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2001, American Mathematical Society

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