Yosida averaging of a semigroup
= Yosida averaging of a semigroup
{c}
For $x$ in the underlying Banach space,
$$
x_t=\frac1t\int_0^tU(s)x\,ds
$$
belongs to the generator domain, satisfies $Ax_t=[U(t)x-x]/t$, and converges to $x$ as $t\downarrow0$.