Content deleted Content added
No edit summary |
|||
Line 30:
==Riesz Representation Theorem==
If <math>u</math> is subharmonic in a region <math>D</math>, in [[Euclidean space]] of dimension <math>n</math>, <math>v</math> is harmonic in <math>D</math>, and <math>u\leq v</math>, then <math>v</math>
is called a harmonic majorant of <math>u</math>. If a harmonic majorant exists, then there exists the least harmonic majorant, and
:<math>u(x)=v(x)-\int_D\frac{d\mu(y)}{|x-y|^{n-2},\quad n\geq 3</math>
while in dimension 2,
:<math>u(x)=v(x)+\int_D\log|x-y|d\mu(y).</math>
This is called the [[Friedrich Riesz|Riesz]] representation theorem.
==Subharmonic functions in the complex plane==
| |||