On the relation between the semigroup and its infinitesimal generator
We prove that for a semigroup generator A the solutions of u′(t) = Au(t) and u(0) = x are completely determined by the resolvent of A along an equidistant sequence (so + nr)nNr∈R, s0∈C, of points in the resolvent set of A. © 1987 American Mathematical Society.
Publication Source (Journal or Book title)
Proceedings of the American Mathematical Society
Neubrander, F. (1987). On the relation between the semigroup and its infinitesimal generator. Proceedings of the American Mathematical Society, 100 (1), 104-108. https://doi.org/10.1090/S0002-9939-1987-0883409-5