Difference between revisions of "Semigroup property of delta exponential"
From timescalewiki
| Line 7: | Line 7: | ||
==References== | ==References== | ||
| − | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta exponential|next=Exponential dynamic equation}}: Lemma 2.31 | + | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta exponential|next=Exponential dynamic equation}}: Lemma $2.31$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 23:19, 8 February 2017
Theorem
Let $\mathbb{T}$ be a time scale, let $t,s \in \mathbb{T}$, and let $p \in \mathcal{R}\left( \mathbb{T},\mathbb{C} \right)$ be a forward regressive function. The following formula holds for all $s,t \in \mathbb{T}$: $$e_p(t,r;\mathbb{T})e_p(r,s;\mathbb{T})=e_p(t,s;\mathbb{T}),$$ where $e_p$ denotes the delta exponential.
Proof
References
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Lemma $2.31$
