# subharmonic function

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## subharmonic function

[¦səb·här′män·ik ′fəŋk·shən]
(mathematics)
A continuous function is subharmonic in a region R of the plane if its value at any point z0 of R is less than or equal to its integral along a circle centered at z0.
References in periodicals archive ?
* 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 [13].
[27], 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.

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