# 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 | ||

[[Category:Theorem]] | [[Category:Theorem]] | ||

[[Category:Unproven]] | [[Category:Unproven]] |

## Revision as of 23:15, 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