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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 $A\sp 2$ 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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