Exact(60)
By virtue of strong continuity of, boundedness of,, is strongly continuous.
The function is strongly continuous.
., for and, is strongly continuous.
Function is strongly continuous and for all.
Therefore, generates a strongly continuous semigroup given by (2.14).
Hence we obtain that is weakly strongly continuous.
But they are true for any strongly continuous linear representation.
(a) The function is strongly continuous and for all and.
The function is strongly continuous and for all and.
Then the operator A generates a strongly continuous semigroup.
with and are strongly continuous on 0 ≤ s ≤ t ≤ a.
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