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The properties of a transformation
by R.S. Phillips, which transforms an exponentially bounded C 0-semigroup of operators T(t) to a Yosida approximation depending on h, are studied. The set of exponentially bounded, continuous functions f: [0, ∞[→ E with values in a sequentially complete L c-embedded space E is closed under the transformation. It is shown that
for certain complex h and k, and that
, where the limit is uniform in t on compact subsets of the positive real line. If f is Hölder-continuous...
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