Abstract
Abstract - The classical proof of the Trotter - Kato theorem also provides rate estimates for smooth initial data. We discuss the possibilities to reduce the so-called smoothness gap for special types of semigroups as, for instance, analytic semigroups. Furthermore, we show that the assumption of stability of the approximating semigroups can be relaxed if at the same time the consistency requirement is replaced by a stronger assumption. Finally, we give a proof for a ‘folk’ theorem for nonhomogeneous problems which repeatedly was proved under stronger assumptions than necessary.
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