Category:Circumferential Means
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This category contains results about Circumferential Means.
Definitions specific to this category can be found in Definitions/Circumferential Means.
Let $D$ be a complex domain.
Let $f: D \to \R$ be a subharmonic function or a superharmonic function.
Let $\map {B^-} {a; r} \subseteq D$ be a closed disk with center $a$ and radius $r$:
The integral over the boundary of $\map {B^-} {a; r}$:
- $\ds \int_0^{2 \pi} \map f {a + r e^{i \theta} } \rd \theta$
is known as the circumferential mean of $f$ over $\map {B^-} {a; r}$.
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