Contraction semigroup
= Contraction semigroup
{title2=$\|S(t)\|\leq1$}
A contraction semigroup is a <strongly continuous semigroup> of bounded <linear operators> satisfying $\|S(t)\|\leq1$ for every $t\geq0$. The <Hille-Yosida theorem> characterizes its <infinitesimal generator of a semigroup> by dense domain, closedness, and the <resolvent> estimates $\|(\lambda-A)^{-n}\|\leq\lambda^{-n}$ for real $\lambda>0$ and integers $n\geq1$.