A counterexample concerning the maximum and minimum of a subharmonic function
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- by Alexander Fryntov PDF
- Proc. Amer. Math. Soc. 122 (1994), 97-103 Request permission
Abstract:
For every $\Delta > 0$ a function u subharmonic in the plane is constructed such that u has the order $\rho = 1 + \Delta$ and satisfies the condition \[ \min \limits _\varphi u(r{e^{i\varphi }})/\max \limits _\varphi u(r{e^{i\varphi }}) \leq - (C + 1)\quad \text {for every} r > 0,\] where $C = C(\rho ) > 0$. This example answers a question of W. K. Hayman.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 97-103
- MSC: Primary 30D20; Secondary 31A05
- DOI: https://doi.org/10.1090/S0002-9939-1994-1189746-5
- MathSciNet review: 1189746