Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A counterexample concerning the maximum and minimum of a subharmonic function


Author: Alexander Fryntov
Journal: Proc. Amer. Math. Soc. 122 (1994), 97-103
MSC: Primary 30D20; Secondary 31A05
MathSciNet review: 1189746
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

$\displaystyle \mathop {\min }\limits_\varphi u(r{e^{i\varphi }})/\mathop {\max }\limits_\varphi u(r{e^{i\varphi }}) \leq - (C + 1)$   for every$\displaystyle \,r > 0,$

where $ C = C(\rho ) > 0$. This example answers a question of W. K. Hayman.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30D20, 31A05

Retrieve articles in all journals with MSC: 30D20, 31A05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1189746-5
PII: S 0002-9939(1994)1189746-5
Keywords: Subharmonic functions, entire functions, positive harmonic function
Article copyright: © Copyright 1994 American Mathematical Society