NDLI: Cluster Values of Bounded Analytic Functions

Content Provider	Scilit
Author	Gamelin, T. W.
Copyright Year	1977
Description	Let D be a bounded domain in the complex plane, and let belong to the topological boundary of D. We prove two theorems concerning the cluster set of a bounded analytic function f on D. The first theorem asserts that values in are assumed infinitely often in every neighborhood of , with the exception of those lying in a set of zero analytic capacity. The second asserts that all values in are assumed infinitely often in every neighborhood of , with the exception of those lying in a set of zero logarithmic capacity. Here is the fiber of the maximal ideal space of lying over , is the Shilov boundary of the fiber algebra, and is the harmonic measure on .
Related Links	http://www.ams.org/tran/1977-225-00/S0002-9947-1977-0438133-8/S0002-9947-1977-0438133-8.pdf
Ending Page	306
Page Count	12
Starting Page	295
ISSN	00029947
e-ISSN	10886850
DOI	10.2307/1997508
Journal	Transactions of the American Mathematical Society
Volume Number	225
Language	English
Publisher	Duke University Press
Access Restriction	Open
Subject Keyword	Mathematical Physics Cluster Values Bounded Analytic Functions Values of Bounded
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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Cluster Values of Bounded Analytic Functions