Commuting semigroups of holomorphic mappings

Details Commuting semigroups of holomorphic mappings Commuting semigroups of holomorphic mappings

2006-09-30

arxiv.org/abs/math/0610027v1

Mathematics

Complex Variables

Scientific paper

Let $S_{1}=\left\{F_t\right\}_{t\geq 0}$ and $S_{2}=\left\{G_t\right\}_{t\geq 0}$ be two continuous semigroups of holomorphic self-mappings of the unit disk $\Delta=\{z:|z|<1\}$ generated by $f$ and $g$, respectively. We present conditions on the behavior of $f$ (or $g$) in a neighborhood of a fixed point of $S_{1}$ (or $S_{2}$), under which the commutativity of two elements, say, $F_1$ and $G_1$ of the semigroups implies that the semigroups commute, i.e., $F_{t}\circ G_{s}=G_{s}\circ F_{t}$ for all $s,t\geq 0$. As an auxiliary result, we show that the existence of the (angular or unrestricted) $n$-th derivative of the generator $f$ of a semigroup $\left\{F_t\right\}_{t\geq 0}$ at a boundary null point of $f$ implies that the corresponding derivatives of $F_{t}$, $t\geq 0$, also exist, and we obtain formulae connecting them for $n=2,3$.

Affiliated with

Also associated with

No associations

Rating

Commuting semigroups of holomorphic mappings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Commuting semigroups of holomorphic mappings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Commuting semigroups of holomorphic mappings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-616440