Are there any other useful semigroups aside from $e^{At}$ $e^{At}$ trivially satisfies both properties of semigroup namely


*

*$T(t+s) = T(t)T(s)$    

*$T(0) = I$


Does there exist any other commonly used operators aside from $e^{At}$ that is a semigroup? Ignoring the obvious ones such as $M^{t}$ where $M \in \mathbb{R}$

More context?  In certain situations, every one-parameter semigroup can be expressed in that way (e.g. every strongly-continuous one-parameter semigroup of bounded operators on a Banach space $X$ has an infinitesimal generator $A$, and thus can be expressed as $\exp(-At)$, where $A$ is a closed densely defined linear operator on $X$).
