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On generators of integrated $$C$$-semigroups and $$C$$-cosine functions. (English) Zbl 0804.47044
Summary: The following two theorems are proved:
(1) the generator of an exponentially equicontinuous $$n$$-times integrated $$C$$-cosine function also generates an exponentially equicontinuous $$[(n+1)/2]$$-times integrated $$C$$-semigroup;
(2) If $$A$$ and $$-A$$ are generators of exponentially equicontinuous $$n$$- times integrated $$C$$-semigroups, then $$A^ 2$$ generates an exponentially equicontinuous $$n$$-times integrated $$C$$-cosine function.

##### MSC:
 47D06 One-parameter semigroups and linear evolution equations 47D09 Operator sine and cosine functions and higher-order Cauchy problems
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##### References:
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