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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.

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