* the law governing the change in the control effect is random and represents a subharmonic function
Then -h extends to be a subharmonic function on D, and there exists a harmonic function k on D and a constant b [greater than or equal to] 0, such that
For a subharmonic function, a generalized Removable Singularity Theorem is described as follows (see [Ra, Theorem 3.6.1]):
Keywords: Holomorphic function, subharmonic function
, Hausdorff measure, exceptional sets.
The authors develop the foundations of potential theory on the Berkovich projective line, including the definition of a measure-valued Laplacian operator, capacity theory, and a theory of harmonic and subharmonic functions
. They also present applications of potential theory on the Berkovcih projective line, especially to the dynamics of rational maps defined over an arbitrary complete and algebraically closed non-Archimedean field K.
Lyubarskii, Frames in the Bargmann space of entire functions and subharmonic functions
. In Entire and Subharmonic Functions
, 167-180, Amer.
HAYMAN, Subharmonic Functions
, Volume 2, Academic Press, 1989.
Specific topics explored include zeros of functions in weighted and Bergman spaces, Blaschke-type conditions for analytic and subharmonic functions
, interpolation sequences for the Bernstein algebra, differentiability of functions of contractions, and free interpolation in the Nevanlinna class.
On subharmonic functions
and differential geometry in the large, Comment.
For a description of subharmonic functions
and their properties, see for example .
, Chapter 2) it then follows that the function [h.sub.max], as the maximum of subharmonic functions
, is again subharmonic in C.
Other topics include Blaschke sets for Bergman spaces, a representation formula for reproducing subharmonic functions
in the unit disc, and the trigonometric obstacle problem and weak factorization.