Uniqueness theorems for subharmonic functions in unbounded domains
Uniqueness theorems for subharmonic functions in unbounded domains
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 <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Omega"> <mml:semantics> <mml:mi …