Subharmonic Function
المؤلف:
Krantz, S. G
المصدر:
"The Dirichlet Problem and Subharmonic Functions." §7.7 in Handbook of Complex Variables. Boston, MA: Birkhäuser,
الجزء والصفحة:
pp. 97-101
27-12-2018
2123
Subharmonic Function
Let 
be an open set and 
a real-valued continuous function on 
. Suppose that for each closed disk 
and every real-valued harmonic function 
defined on a neighborhood of 
which satisfies 
on 
, it holds that 
on the open disk 
. Then 
is said to be subharmonic on 
(Krantz 1999, p. 99).
1. If 
are subharmonic on 
, then so is 
.
2. If 
is subharmonic on 
and 
is a constant, than 
is subharmonic on 
.
3. If 
are subharmonic on 
, then ![max<span style=]()
{f_1(z),f_2(z)}" src="http://mathworld.wolfram.com/images/equations/SubharmonicFunction/Inline23.gif" style="height:14px; width:103px" /> is also subharmonic on 
.
REFERENCES:
Krantz, S. G. "The Dirichlet Problem and Subharmonic Functions." §7.7 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 97-101, 1999.
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