Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

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


Uniqueness theorems for subharmonic functions in unbounded domains

Author: S. J. Gardiner
Journal: Proc. Amer. Math. Soc. 99 (1987), 437-444
MSC: Primary 31B05
MathSciNet review: 875377
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A theorem of Carlson says that a holomorphic function of exponential growth in the half-plane cannot approach zero exponentially along the boundary unless it vanishes identically. This paper presents a generalization of this result for subharmonic functions in a Greenian domain $ \Omega $, using the Martin boundary, minimal fine topology and PWB solution to the $ h$-Dirichlet problem. Applications of the general theorem to specific choices of $ \Omega $, such as the half-space and strip, are presented in later sections.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 31B05

Retrieve articles in all journals with MSC: 31B05

Additional Information

PII: S 0002-9939(1987)0875377-7
Article copyright: © Copyright 1987 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia